The sum to infinity of the series `1/2.4+1/4.6+1/6.8+1/8.10+.......` is

Explanation

To find the sum to infinity of the series \( S = \frac{1}{2 \cdot 4} + \frac{1}{4 \cdot 6} + \frac{1}{6 \cdot 8} + \frac{1}{8 \cdot 10} + \ldots \), we can follow these steps:

### Step 1: Identify the general term of the series
The series can be expressed in terms of a general term. Observing the pattern, we can denote the \( n \)-th term as:
\[ a_n = \frac{1}{(2n)(2n + 2)} \]
for \( n = 1, 2, 3, \ldots \).
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