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anonymous
 5 years ago
i need some help with infinite series! i don't understand :(
anonymous
 5 years ago
i need some help with infinite series! i don't understand :(

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what in particular? convergence?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah, the homeworks says to "find exact values for the first four partial sums, find a closed form for the nth partical sum, and determine whether the series converges by calculating the limit of the nth partial sum. if the series converges, then state its sum" i have a feeling it's easy and i'm just misunderstanding the basics

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the first question is " 2+2/5+2/5^2+...+ 2/ 5^k1"

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok, that is actually a geometric series, so for the limit of the sum, use the finite geometric series formula

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\sum_{0}^{k1}2*(1/5)^n\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0finite geometric sum formula is a(1r^n)/(1r) where r is ratio and a is 1st term (in this case a=2 and r=1/5

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0when you take the limit, since r is less than 1, the r^n term is gonna get smaller and smaller and eventually disappear, which leaves the much easier formula of just a/(1r) or in this case 2/(11/5)=2/(4/5) multiply by reciprocal of the bottom and reduce and you should get 5/2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wow! thanks for saving my life. you're the best :)
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