- #1

thercias

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## Homework Statement

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

## Homework Equations

## The Attempt at a Solution

finding derivative of the function multiplied by x

d/dx(xS(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.