Question

Express the series using sigma notation. 2 - 6 + 18 – 54 + 162 ...

Answer 1

$2-6+18-54+162+\cdots=2(-3)^0+2(-3)^1+2(-3)^2+2(-3)^3+2(-3)^4+\cdots$
$=\displaystyle2\sum_{n=0}^\infty(-3)^n$