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Type I -- Infinite Summation


ballon

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  • 2 weeks later...

we have the same IA that was given last year. if anyone couullld pleeaassseeeeeee give me a sample IA that they did last year it would be awesome :D thxx

There's a fine line between asking for help and asking for the answers.

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Sn=a^x meaning if a=3 and x=3 the sum is 27. You get this from the property of logarithms where you pull out the exponent. So from t1=(x ln a)/1, the x is just pulled out from it's actual exponential spot.

3 ln 3= ln 3^3

can you explaın how can you fınd this? ı dont understand.please help me

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umm.. for the first task when x=1 and we are meant to find S10 for various positive values of a. i tried a=0.02. the values i get for Sn are alternating positive and negative values. for eg. for S2 i get..2.343 but then for S3 i get something like -0.288. the graph is not exponential but zigzag however the values eventually do lead up to 0.02. is that normal? or am i doing something wrong?

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yeahh i get it :D thxx

umm some people were actually saying that that is not a limitation because it still complies with the general statement that we are trying to find. that as n approaches infinity the value of Sn = a. s is it still a limitation??

smart. this is actually your limitation. when a=0.02 you don't find a pattern similar to previous, which means a cannot be 0.02 in this task. then generalise the limitation if you know what I mean. do you know what I mean?

If one works out T9(0.2,1). T9=0.2, which proves the general statement of a^x. It is true that it has a different pattern but it does approach the general statement. so why is it than a limitation?

and any ideas about the scope of the general statement? D:

what does that even mean?

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OK, so I've read through this thread trying to figure out how to find the both general statements required in this portfolio. I know what they both are, but I did it through just examining my data... It was fairly obvious when I looked at it. I keep reading about the Taylor Series and derivatives and stuff, but we haven't done calculus yet, so it makes no sense to me (at least I think that stuff is calculus). Like, for the first general statement on the first page of the portfolio, when x has been kept at 1, I know the general statement (not 100% clear if I'm just allowed to post the general statements or not...), but I did it because I just looked at the asympototes the graph produced, and what number I kept consistently getting when I calculated S10 I knew what the general statemtent was, but how do I mathematically prove it without just reasoning it or calculus... If I can post the general statements, let me know so my question can be more clear...

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hmmm I've tried to work out so many IAs that I forgot which one needs what method, but if I remember correctly, this task should not require calculus :/

actually you are not allowed to post any answer (which includes general statements) here but some people still did -_- haha if you like you can PM me or anybody whom you think could help you.

actually there are various methods, depending on how you see it. I'd say the easiest is the graphical method (plotting your data and finding the best regression). or, as you might have guessed, using that Taylor thing.

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OK, so I can just use the Taylor Series to calculate the first general statement... Can I just use the Taylor Series for the second one they ask on the second page? They ask for two; one for when x=1 and the other for when x can be anything. I see how I can use the Taylor Series to find the general statement when x=1, but I'm not so sure how to use it for the other one. Also, we were never actually taught the Taylor Series in our class; is it OK for me to just say the series given in this portfolio is an example of the Taylor Series, and then provide a footnote for where I got the Taylor Series from, and then solve for the general statements?

Any help is much appreciated.

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