Question

Write the sum in sigma notation. $ \noindent 1 - x + x^2 - x^3 + \cdot\cdot\cdot + {(-1)}^n x^n $

Answer 1

$1-x+x^2-x^3...+(-1)^nx^n=\sum\limits_{n=0}^{\infty}(-1)^nx^n=\sum\limits_{n=1}^{\infty}(-1)^{n-1}x^{n-1}$