The sum of the series `5/(1. 2.3)+7/(3. 4.5)+9/(5. 6.7)+` ....is equal to

Options

A. `log(8//e)`
B. `log(e//8)`
C. log 8e
D. log 8

Explanation

To find the sum of the series \( S = \frac{5}{1 \cdot 2 \cdot 3} + \frac{7}{3 \cdot 4 \cdot 5} + \frac{9}{5 \cdot 6 \cdot 7} + \ldots \), we will first identify the general term of the series and then simplify it using partial fractions.

### Step 1: Identify the general term
The \( n \)-th term of the series can be expressed as:
\[ t_n = \frac{2n + 3}{(2n - 1)(2n)(2n + 1)} \]
This is derived from observing the pattern in the numerators and denominators.
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