# Infinite Infinities

Algebra Level 3

$2\sum _{ n=0 }^{ \infty }{ { \left[ { 2\left[ \frac { 2 \sum _{ n=0 }^{ \infty }{ { \left[ { 2\left[ \frac { 2 \sum _{ n=0 }^{ \infty }{ { \left[ { 2\left[ \frac { ... }{ 2013 } \right] }^{ n } \right] }^{ -1 } } }{ 2013 } \right] }^{ n } \right] }^{ -1 } } }{ 2013 } \right] }^{ n } \right] }^{ -1 } }$

What is the value of the nested summation above?

×