Question

show that In(1+x)=x-x^2/2+x^3/3-x^4/4+⋯

Answer 1

Can we assume \(\dfrac{1}{1-x} = 1 + x + x^{2} + x^{3} + ...\)?

Answer 2

what @tkhunny said
take the derivative, integrate term by term

Answer 3

ok

Answer 4

Well, you may wish to substute -x, first, giving \(\dfrac{1}{1+x} = 1 - x + x^{2} - x^{3} + ...\)