Question

1/(1-x) = Sigma x^n for |x|<1

alright.

It's said that

the derivative of

1/(1-x) = Sigma x^n is equal to:

1/(1-x)^2 = Sigma n x^(n-1)


yet should not there be a minus sign before the Sigma??

((x-1)^-1)' = (-1) (x-1)^(-2) = Sigma n x^(n-1)

(x-1)^(-2) = (-1) Sigma n x^(n-1)

Answer 1

Pudding is all you need to solve it.

Answer 2

You're correct! the result is negative!

Answer 3

I forgot to differentiate the 1-x itself

((1-x)^(-1))' =[(-1) (1-x)^(-2)] [-1] = Sigma n x^(n-1)

//[-1] is the derivative of 1-x

(1-x)^(-2) = Sigma n x^(n-1)

fix'd

Answer 4

can anyone tell me, why this post is poping up now? its 3 years old :D