Question

solve this logarithm question​

Answer 1

Answer:

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

Step-by-step explanation:

$log_{a} \: {b}^{n} \: = n \: log_{a} \: b \\ log_{a} \: a = 1$

$log_{2}2 + log_{2} \: {2}^{2} + log_{2} \: {2}^{3 } + ....... + log_{2} \: {2}^{n} \\ = log_{2}2 + 2 log_{2}2 + 3 log_{2}2 + ........ + n log_{2}2 \\ = 1 + 2 + 3 + ........ + n \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\: first \: term \: = 1 \\ common \: difference \: = 1 \\ last \: term \: = \: n$

$s_{n} = \frac{n}{2} (first \: term \: + last \: term) \\ = \frac{n}{2} (1 + n) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$