Question

Find the Value of the following

Answer 1

Step-by-step explanation:

We have,

$log_{2}(2) + log_{2}(2^{2} ) +log_{2}(2^{3}) + .... + log_{2}(2^{n} )$

$= log_{2}(2.2^{2}.2^{3} ....2^{n})$

$= log_{2}(2^{1 + 2 + 3 + ... + n})$

$= log_{2}(2^{ \frac{n(n + 1)}{2} })$

$= \frac{n(n + 1)}{2}$