Hi all. I have been asked to sum this series:
1+4x+7x^2+10x^3+...+(3N-2)x^N
and also asked what the sum is to infinity when |x|< 1
I have all of the formulae (dodgy spelling ) for summing a series and sum to infinity but this one has me stumped; mainly because at the back of the text book the given anser is:
[3/(1-x)^2]-[2/(1-x)]
I just don't know how to get this answer. It's caused a bit of a mental block for me and his becoming quite annoying! Any help on working through to get this answer would be really helpful and much appreciated. Thanks in advance!
Where you have factorised and brought out (1+3x), can you do that? Because if you multiplied out those brackets you wouldn't get what you factorised in the first place... I can see your working through though. Just that one point that has confused me a little.
EDIT: also @mr.fantastic i'm not sure it was a typo, that is exactly as written in the text book, unless of course it's typed incorrectly in there! Also, where you have seperated the two sums. Is it possible to take the right summation and change it into the form where you start at i=0 up to i and then x^i-1 becomes just x^i. Because then from there I know what that sum is but can you then subtract the two different answers although they are 'summed' in a slightly different form? THanks for your help so far
EDIT 2: @soropan sorry about that just realised how you have written it. Makes sense now and I agree with what you have given me. Thankyou very much for your quick and friendly response! One point to make actually, could you not just work out the sum for 1+3x+3x^2.... instead of factorising?