Question

need help with series agian

Answer 1

starting with \[\sum_{1}^{\infty} x ^{n}\]


\[\sum_{1}^{\infty} nx ^{n-1}\]
|x|<1

find the sum of series.
Again no clue what should be done here

Answer 2

notice that sum of geometric series with \(|x|<1\) is \[\sum_{n=0}^{\infty} x ^{n}=1+x+x^2+...=\frac{1}{1-x}\]hint: take derivative of both sides

Answer 3

i took but it not help me

Answer 4

the first sum = 1/(1-x)
the second sum is the derivative of the first sum
(derivative of the sum is the sum of derivatives)
so differentiate 1/(1-x)