Question

Calculate `A`, where `A = 2 + 2xx2 + 2xx2xx2 + 2xx2xx2xx2 + ... + 2xx2 ... 2xx2` (the last number has 2013 digits 2)?

Answer 1

`A= (2(1 - 2^2013))/(1 - 2)`

Explanation:

This is represented by

`sum_(n = 1)^2013 2^n`

This is a geometric series of common ratio `2` and first term `2`.

`S_n = (2(1 - 2^2013))/(1 - 2)`

This is very large so I won't even try evaluating.

Hopefully this helps!