This is a geometric series with first term 2 and common ratio -4. The general term of such a series (an) in terms of the first term (a1) and common rato (r) is written as
an = a1*r^(n-1)
The sum is the sum of such terms.
[tex]sum=\sum\limits_{n=1}^{\infty}{2(-4)^{(n-1)}}[/tex]
