Show that 1- x/2 + x^2/3 - x^3/4 + x^4/5.... (-1)^n (x^n)/(n+1) = ln(1+x)/x
with |x| < 1
The Attempt at a Solution
finding derivative of the function multiplied by x
= 1 -x + x^2 - x^3 + x^4 - x^5 +....
absolute value of this function = 1 + x + x^2 + x^3 + x^4.... = 1/1-x ( geometric series)
the integral of that gives us -ln(1-x) + c
drawing a blank now. not really sure where to go.