Question

Help with geometric series

Answer 1

I have a theorem that says.

Suppose\[a_0≠0.\]
The geometric series
\[\sum_{n=0}^{∞}r^na_0\]
converges if |r|<1 and diverges if |r|≥1. When |r|<1 the sum is provides by
\[\sum_{n=0}^{∞}r^na_0=\frac{ a_0 }{ 1-r }.\]
Can someone help me find the sum of \[\sum_{n=0}^{∞}(2n-1)(2x)^n\]
for all x in the interval of convergence. I know the power series convergence for -1/2<x<1/2

Answer 2

try distributing first

Answer 3

\[\sum_{n=0}^{∞}(2n-1)(2x)^n=\sum_{n=0}^{∞}2n(2x)^n-\sum_{n=0}^{∞}(2x)^n\]
???

Answer 4

yes you are fast ;)

Answer 5

now look for a sum n*x^n, i believe its like a derivative of some expression

Answer 6

also take out the 2

Answer 7

I'm not quite with you

Answer 8

heres a good resource to get you started http://answers.yahoo.com/question/index?qid=20100425142446AATBAsX