The sum of the series: `1/((log)_2 4)+1/((log)_4 4)+1/((log)_8 4)++1/((log)_(2^n)4)` is
`(n(n+1))/2` (b) `(n(n+1)(2n+1))/(12)` (c) `(n(n+1))/4` (d) none of these

Explanation

To find the sum of the series \( S = \frac{1}{\log_2 4} + \frac{1}{\log_4 4} + \frac{1}{\log_8 4} + \ldots + \frac{1}{\log_{2^n} 4} \), we can follow these steps:

### Step 1: Rewrite the logarithmic terms
We know that the change of base formula for logarithms states:
\[ \log_a b = \frac{\log_c b}{\log_c a} \]
Using this, we can rewrite each term in the series:
...