Question

\[\begin{aligned}n&:=2 + 4 + 8 + 16 \cdots\\ \iff n&= 2(1 + 2 + 4 + 8 + 16)\cdots \\ \iff n &= 2(n + 1) \\ \iff n & = -1\end{aligned}\]

Answer 1

the sum is a/r-1
2/2-1
2

Answer 2

its an infinte gp series

Answer 3

^yeah. and that's why you cannot subtract 2n and n to get n. It's like saying
\[2\infty -\infty = \infty \]
you just can't do that.