Question

Prove that for -1 < x < 1 ......

Answer 1

1/(1+x) = \[\sum_{n=0}^{\infty} (-1)^{n} x ^{n} = 1 - x + x ^{2} - x ^{3} ...\]

Answer 2

\[\ln (1+x) = \sum_{n=1}^{\infty} (-1)^{n-1} x ^{n} / (n) = x - x^{2}/2 + x ^{3}/3 -x ^{4}/4 +...\]