flinquinnster Posted August 23, 2013 Report Share Posted August 23, 2013 I'm getting particularly stuck on a convergence question from an option topic (series and differential equations - still old syllabus pre-2014). If anybody can shed light on how line 2 becomes 3, that would be much appreciated. I don't get how the cube root becomes that infinite series! The question should also be attached as well.Ah, Maths HL. This option topic/paper 3 makes me regret it all... 2 Reply Link to post Share on other sites More sharing options...
Lero Posted August 23, 2013 Report Share Posted August 23, 2013 This dreaded question, I remember encountering this and never having solved it. Is this a really old question that may have been a part of the previous syllabus back in '05 or '06? 1 Reply Link to post Share on other sites More sharing options...
flinquinnster Posted August 23, 2013 Author Report Share Posted August 23, 2013 Wow, it's reassuring to know that somebody else has gotten stuck on this! This is from a May'08 paper, so it should be new syllabus, weirdly enough. I honestly don't think that there are any infinite series we are given for cube root expansions or fractional power expansions, so I don't get how this line comes about. I was maybe thinking some kind of Maclaurin expansion, but that doesn't seem right either. I think I've seen similar questions as this as some kind of fractional binomial expansion, but I honestly don't know. I think that I'm just going to leave this question, despite the examiners' report suggesting that all this question took was some simple 'algebraic manipulation'. Reply Link to post Share on other sites More sharing options...
Rahul Posted September 5, 2013 Report Share Posted September 5, 2013 Oh my. That... does not make sense to me whatsoever. I'll run it by my math teacher in the next couple days though. Reply Link to post Share on other sites More sharing options...
flinquinnster Posted September 5, 2013 Author Report Share Posted September 5, 2013 I think I've figured this out - you use the binomial expansion for fractional powers to get an infinite series. That accounts for how line 2 turns into line 3. I have a link here with the formula - scroll down. Hope that this never gets put into another exam! Reply Link to post Share on other sites More sharing options...
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