Question

If it is known that 1+x+x² + x^3 +..... + x^n-1=
$\frac{1 - x ^{n} }{1 - x}$

, sum the series 1 + 2x + 3x^2 + ... +(n-1)x^n-2
​

Answer 1

sorry I done wrong

now given s=1+2x+3x*2.......(n-1)x*n-2

now multiply by x

Sx=x+2x*2+3x*3+........(n-1)x*n-1

s-sx=1+x+x*2+x3......x*n-1

you know that 1+x+x*2+x3......x*n-1=1-x*n/1-x

s-sx=1-x*n/1-x

s(1-x)=1-x*n/1-x

s=1-x*n/(1-x)*2

sorry for inconvenience