Question

The sum of the series `log_4 2 - log_8 2 + log_16 2 + ...............` to `oo` is

Options

• `1 - log_e 2`

• `1 + log_e 2`

• `log_e 2 - 1`

• `log_2 e`

Answer 1

`1 - log_e 2`

Explanation:

`log_4 2 - log_8 2 + log_16 2`.........

= `log_(2^(2)) 2 - log_(2^(3)) 2 + log_(2^(4)) 2`.........

= `1/2 - 1/3 + 1/4`.......

= `- (1 - 1/2 + 1/3 + 1/4 + .......) + 1`

= `1 - log_e 2`