1. Tardigrade
  2. Question
  3. Mathematics
  4. If S ∞=(1/1 ⋅ 3 ⋅ 5 ⋅ 7 ⋅ 9)+(1/3 ⋅ 5 ⋅ 7 ⋅ 9.11)+(1/5 ⋅ 7 ⋅ 9 ⋅ 11 ⋅ 13) + ldots, then the value of (1/120 S ∞) is

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Q. If $S _{\infty}=\frac{1}{1 \cdot 3 \cdot 5 \cdot 7 \cdot 9}+\frac{1}{3 \cdot 5 \cdot 7 \cdot 9.11}+\frac{1}{5 \cdot 7 \cdot 9 \cdot 11 \cdot 13}$ $+\ldots$, then the value of $\frac{1}{120 S _{\infty}}$ is

Sequences and Series

Solution:

$T_{n}=\frac{1}{(2 n-1)(2 n+1) \ldots .(2 n+7)}$
$\therefore S _{\infty}=\frac{1}{120 \times 7}$
$\Rightarrow 120\, S _{\infty}=\frac{1}{7}$