Binomial Theorem/Examples/Square Root of 2

Example of Use of Binomial Theorem

 * $\sqrt 2 = 2 \paren {1 - \dfrac 1 {2^2} - \dfrac 1 {2^5} - \dfrac 1 {2^7} - \dfrac 5 {2^{11} } - \cdots}$

Proof
The first few terms of the real sequence are:
 * $2, \dfrac 3 2, \dfrac {23} {16}, \dfrac {91} {64}, \dfrac {1451} {1024}, \dotsc$