dessskris Posted July 21, 2011 Report Share Posted July 21, 2011 is it t0+t1+.....+tn? yes. Also,how to graph the relation between sn and n when we just only know x=1?thanks~~ what is meant by that is... for example: when n=0, S0=T0 when n=1, S1=T0+T1 when n=2, S2=T0+T1+T2 ... Sn=T0+T1+T2+...+Tn you calculate each of it... then plot it in a scatter graph! Reply Link to post Share on other sites More sharing options...
iloveushrek13 Posted July 21, 2011 Report Share Posted July 21, 2011 is it t0+t1+.....+tn? yes. Also,how to graph the relation between sn and n when we just only know x=1?thanks~~ what is meant by that is... for example: when n=0, S0=T0 when n=1, S1=T0+T1 when n=2, S2=T0+T1+T2 ... Sn=T0+T1+T2+...+Tn you calculate each of it... then plot it in a scatter graph! yes , i know it!~~~~thanks~~~but when x-1,i dont know what is a,so t2=(lna)^2/3! then,how to plot the graph?i still dont know~~TAT Reply Link to post Share on other sites More sharing options...
dessskris Posted July 21, 2011 Report Share Posted July 21, 2011 oh lol you try for various values of a (e.g. 1, 2, 3, 4) and you have each curve for each value of a and x (a and x don't have to be the same). Reply Link to post Share on other sites More sharing options...
iloveushrek13 Posted July 21, 2011 Report Share Posted July 21, 2011 oh lol you try for various values of a (e.g. 1, 2, 3, 4) and you have each curve for each value of a and x (a and x don't have to be the same). oh yeah~~~i got it~~~i didn't look at the questions carefully just now~~~~thanks a lot~~~terima kasih~~~XDDD so how many value should i try?should it all be positive integar?or i should try negative integar or zero or anything else when is in testing the validity of the general statement?thanks~~~XP Reply Link to post Share on other sites More sharing options...
dessskris Posted July 21, 2011 Report Share Posted July 21, 2011 lol terima kasih kembali umm I'd say between 3 to 5 values would be optimal... more would be good, but I don't think that would make your IA any better because it's just making it so much longer than it should be well, that's up to you try to vary the value of a and x, so you may try negative integers and zeroes or even decimals and if it doesn't work, it means there is a limitation Reply Link to post Share on other sites More sharing options...
iloveushrek13 Posted July 21, 2011 Report Share Posted July 21, 2011 lol terima kasih kembali umm I'd say between 3 to 5 values would be optimal... more would be good, but I don't think that would make your IA any better because it's just making it so much longer than it should be well, that's up to you try to vary the value of a and x, so you may try negative integers and zeroes or even decimals and if it doesn't work, it means there is a limitation haha...thanks a lot~~~XDDD but how it will be y=a^x??by guessing??or the graph?? Reply Link to post Share on other sites More sharing options...
dessskris Posted July 21, 2011 Report Share Posted July 21, 2011 by the graph of course. or there is another method that uses algebra (hence more mathematical and is better IMO) to prove it too. there is no guessing in math, unless you are able to prove it later. Reply Link to post Share on other sites More sharing options...
iloveushrek13 Posted July 21, 2011 Report Share Posted July 21, 2011 by the graph of course. or there is another method that uses algebra (hence more mathematical and is better IMO) to prove it too. there is no guessing in math, unless you are able to prove it later.ohh....can i say the graph look like y=a^x,then i sub some numbers into y=a^x to prove it??XDD Reply Link to post Share on other sites More sharing options...
dessskris Posted July 21, 2011 Report Share Posted July 21, 2011 no you can't... what you can do is observing the patterns in various values of a and x and generalising it. Reply Link to post Share on other sites More sharing options...
iloveushrek13 Posted July 22, 2011 Report Share Posted July 22, 2011 no you can't... what you can do is observing the patterns in various values of a and x and generalising it.so you mean,i have to say:from the graph above ,the function is y=a^x?I just don't really know how to write it. Reply Link to post Share on other sites More sharing options...
dessskris Posted July 22, 2011 Report Share Posted July 22, 2011 still no... okay example. when a=1 and when x=1, S∞ is 1. when a=1 and when x=2, S∞ is 2. when a=1 and when x=3, maybe S∞ is 3. so far you can see some sort of pattern..? then... when a=2 and when x=1, S∞=2. when a=2 and when x=2, S∞=4. when a=2 and when x=3, maybe S∞=8. now you can see the pattern more clearly..? when a=3 and when x=1, S∞=3. when a=3 and when x=2, S∞=9. when a=3 and when x=3, maybe S∞=27. does the pattern become much clearer now? do some calculation related to the above observation. (is that correct, btw? I just did it based off memory and logic..) and in the end you will get S∞=a^x Reply Link to post Share on other sites More sharing options...
iloveushrek13 Posted July 22, 2011 Report Share Posted July 22, 2011 still no... okay example. when a=1 and when x=1, S∞ is 1. when a=1 and when x=2, S∞ is 2. when a=1 and when x=3, maybe S∞ is 3. so far you can see some sort of pattern..? then... when a=2 and when x=1, S∞=2. when a=2 and when x=2, S∞=4. when a=2 and when x=3, maybe S∞=8. now you can see the pattern more clearly..? when a=3 and when x=1, S∞=3. when a=3 and when x=2, S∞=9. when a=3 and when x=3, maybe S∞=27. does the pattern become much clearer now? do some calculation related to the above observation. (is that correct, btw? I just did it based off memory and logic..) and in the end you will get S∞=a^x ohhh~~~~~~~~i understand~~~XDDD thanks!!!!!!is correct!!!thanks ya~~~~ Reply Link to post Share on other sites More sharing options...
little penguin Posted July 25, 2011 Report Share Posted July 25, 2011 I'm at the second part, and I'm finding various values for T9 (a,x). To calculate this value, I type in each number in the sequence and then press enter (so I'd have to type 1 + 2ln2 + (2ln2)^2/2! + ... all the way up to (2ln2)^9/9!). This is incredibly time consuming. I was wondering if there is any more efficient way to find the T9 values? Maybe plugging in something into "Y=" and using something fancy to find the result?Someone suggested taking a screenshot of my calculations and putting in the portfolio, but I can't imagine how that can be reasonable with the method I'm using now. It's just too long.I have a TI-84 Plus, btw. Reply Link to post Share on other sites More sharing options...
iloveushrek13 Posted July 29, 2011 Report Share Posted July 29, 2011 (edited) still no... okay example. when a=1 and when x=1, S∞ is 1. when a=1 and when x=2, S∞ is 2. when a=1 and when x=3, maybe S∞ is 3. so far you can see some sort of pattern..? then... when a=2 and when x=1, S∞=2. when a=2 and when x=2, S∞=4. when a=2 and when x=3, maybe S∞=8. now you can see the pattern more clearly..? when a=3 and when x=1, S∞=3. when a=3 and when x=2, S∞=9. when a=3 and when x=3, maybe S∞=27. does the pattern become much clearer now? do some calculation related to the above observation. (is that correct, btw? I just did it based off memory and logic..) and in the end you will get S∞=a^x how to write a conclusion??need to include what information?thanks... Also,I get this a x n t9(5,3) 5 3 0 1.000000 1.000000 1 4.828314 5.828314 2 11.656307 17.484621 3 18.760102 36.244723 4 22.644915 58.889637 5 21.867350 80.756988 6 17.597071 98.354059 7 12.137740 110.491799 8 7.325602 117.817402 9 3.930034 121.747436 this does not valid to a^X...will this be a limitation??i'm confused...(sorry for giving anything it shouldn't be)....need help~~~ Edited July 29, 2011 by iloveushrek13 Reply Link to post Share on other sites More sharing options...
dessskris Posted July 29, 2011 Report Share Posted July 29, 2011 I'm at the second part, and I'm finding various values for T9 (a,x). To calculate this value, I type in each number in the sequence and then press enter (so I'd have to type 1 + 2ln2 + (2ln2)^2/2! + ... all the way up to (2ln2)^9/9!). This is incredibly time consuming. I was wondering if there is any more efficient way to find the T9 values? Maybe plugging in something into "Y=" and using something fancy to find the result? Someone suggested taking a screenshot of my calculations and putting in the portfolio, but I can't imagine how that can be reasonable with the method I'm using now. It's just too long. I have a TI-84 Plus, btw. this is probably kinda late, but you can use Excel for that. it makes everything simple. if you need the Excel formulas, dig for the old posts, I swear I've posted it some time last January/February. how to write a conclusion??need to include what information?thanks... Also,I get this TABLE REMOVED this does not valid to a^X...will this be a limitation??i'm confused...(sorry for giving anything it shouldn't be)....need help~~~ your final conclusion? you should re-state the general statements and the limitations, and a general pattern observed in the graph. btw you're not allowed to post that table here because some lazy lad can just grab and steal it without working it out in advance. your first column is n right? then what's on the 2nd and 3rd columns? T9 and S9? hmmm actually a^x is not S9, it's S∞ so if you actually continue to find T10, T11 and so on and so forth you'll find that its value approaches 125 so it's not a limitation. Reply Link to post Share on other sites More sharing options...
iloveushrek13 Posted July 29, 2011 Report Share Posted July 29, 2011 I'm at the second part, and I'm finding various values for T9 (a,x). To calculate this value, I type in each number in the sequence and then press enter (so I'd have to type 1 + 2ln2 + (2ln2)^2/2! + ... all the way up to (2ln2)^9/9!). This is incredibly time consuming. I was wondering if there is any more efficient way to find the T9 values? Maybe plugging in something into "Y=" and using something fancy to find the result? Someone suggested taking a screenshot of my calculations and putting in the portfolio, but I can't imagine how that can be reasonable with the method I'm using now. It's just too long. I have a TI-84 Plus, btw. this is probably kinda late, but you can use Excel for that. it makes everything simple. if you need the Excel formulas, dig for the old posts, I swear I've posted it some time last January/February. how to write a conclusion??need to include what information?thanks... Also,I get this TABLE REMOVED this does not valid to a^X...will this be a limitation??i'm confused...(sorry for giving anything it shouldn't be)....need help~~~ your final conclusion? you should re-state the general statements and the limitations, and a general pattern observed in the graph. btw you're not allowed to post that table here because some lazy lad can just grab and steal it without working it out in advance. your first column is n right? then what's on the 2nd and 3rd columns? T9 and S9? hmmm actually a^x is not S9, it's S∞ so if you actually continue to find T10, T11 and so on and so forth you'll find that its value approaches 125 so it's not a limitation. oh....sorry~~~~ is my table correct??what about when a=10,x=5,the table i get doenst match a^x....thanks... Reply Link to post Share on other sites More sharing options...
dessskris Posted July 29, 2011 Report Share Posted July 29, 2011 no need to sorry! please remove the table in your post btw well I didn't do this task so I didn't calculate the Tn and Sn for each value of a and x so I can't tell you if it's right or wrong I only worked it out for one example, plotted the graph to see the trend and worked algebraically to find the general solution. what do you mean by it doesn't match a^x? perhaps it's due to the same reason as previous? Reply Link to post Share on other sites More sharing options...
iloveushrek13 Posted July 29, 2011 Report Share Posted July 29, 2011 no need to sorry! please remove the table in your post btw well I didn't do this task so I didn't calculate the Tn and Sn for each value of a and x so I can't tell you if it's right or wrong I only worked it out for one example, plotted the graph to see the trend and worked algebraically to find the general solution. what do you mean by it doesn't match a^x? perhaps it's due to the same reason as previous? hahaha....never mind...i already got that~~ should i include a,x,n,tn,tn(a,x) into the table?thanks btw.. Reply Link to post Share on other sites More sharing options...
dessskris Posted July 29, 2011 Report Share Posted July 29, 2011 hahaha....never mind...i already got that~~ should i include a,x,n,tn,tn(a,x) into the table?thanks btw.. um, do you tabulate the data separately? if so then you can put one big heading/caption saying "When a=something and x=something" for every table, then in the table just put n, tn, Tn(a, x). that would look better in my opinion. Reply Link to post Share on other sites More sharing options...
iloveushrek13 Posted July 29, 2011 Report Share Posted July 29, 2011 hahaha....never mind...i already got that~~ should i include a,x,n,tn,tn(a,x) into the table?thanks btw.. um, do you tabulate the data separately? if so then you can put one big heading/caption saying "When a=something and x=something" for every table, then in the table just put n, tn, Tn(a, x). that would look better in my opinion. hahaha.......i am doing the data seperately...i'm doing the table just like what you said....hahah........i thought i was wrong before.... thanks~~~ Reply Link to post Share on other sites More sharing options...
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