Question

MEDAL- how do I solve these ?

Answer 1

could I use a/1-r?

Answer 2

if it was in the form a*r^(n-1), you could, but that n out front is throwing everything off

Answer 3

\[\Large \sum_{n = 1}^{\infty}nx^{n-1} = 1x^{1-1}+2x^{2-1}+3x^{3-1}+4x^{4-1}+5x^{5-1}+\ldots\]
\[\Large \sum_{n = 1}^{\infty}nx^{n-1} = x^{0}+2x^{1}+3x^{2}+4x^{3}+5x^{4}+\ldots\]
\[\Large \sum_{n = 1}^{\infty}nx^{n-1} = 1+2x+3x^{2}+4x^{3}+5x^{4}+\ldots\]
That's all I can get for part (a). I'm probably missing something. This probably has something to do with taylor series, but I'm drawing a blank

Answer 4

this page may help

http://math.stackexchange.com/questions/647587/sum-of-a-power-series-n-xn