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

Question

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 (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Tn=(1/(2 n-1)(2 n+1) ldots .(2 n+7)) ∴ S ∞=(1/120 × 7) ⇒ 120 S ∞=(1/7)

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