Question

i need some help with infinite series! i don't understand :(

Answer 1

what in particular? convergence?

Answer 2

yeah, 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

Answer 3

the first question is " 2+2/5+2/5^2+...+ 2/ 5^k-1"

Answer 4

ok, that is actually a geometric series, so for the limit of the sum, use the finite geometric series formula

Answer 5

\[\sum_{0}^{k-1}2*(1/5)^n\]

Answer 6

finite geometric sum formula is a(1-r^n)/(1-r)

where r is ratio and a is 1st term (in this case a=2 and r=1/5

Answer 7

when 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/(1-r) or in this case 2/(1-1/5)=2/(4/5)

multiply by reciprocal of the bottom and reduce and you should get 5/2

Answer 8

wow! thanks for saving my life. you're the best :)