1 + frac{4^2}{3!} + frac{4^4}{5!} + dots inft | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the given series be $S = 1 + \frac{4^2}{3!} + \frac{4^4}{5!} + \dots \infty$. Multiplying and dividing by $4$,we get: $S = \frac{1}{4} \left(

Vedclass · Accepted Answer

$\frac{e^4 - e^{-4}}{8}$

Vedclass · Answer

(D) Let the given series be $S = 1 + \frac{4^2}{3!} + \frac{4^4}{5!} + \dots \infty$. Multiplying and dividing by $4$,we get: $S = \frac{1}{4} \left( 4 + \frac{4^3}{3!} + \frac{4^5}{5!} + \dots \infty \right)$. We know that the expansion of $\sinh(x) = \frac{e^x - e^{-x}}{2} = x + \frac{x^3}{3!} + \frac{x^5}{5!} + \dots \infty$. Substituting $x = 4$,we get: $S = \frac{1}{4} \left( \sinh(4) \right) = \frac{1}{4} \left( \frac{e^4 - e^{-4}}{2} \right) = \frac{e^4 - e^{-4}}{8}$.

$1 + \frac{4^2}{3!} + \frac{4^4}{5!} + \dots \infty = $

Similar Questions

In the expansion of $(1 + x + x^2)e^{-x}$,the coefficient of $x^2$ is

$\frac{1}{2} + \frac{1}{4} + \frac{1}{8 \times 2!} + \frac{1}{16 \times 3!} + \frac{1}{32 \times 4!} + \dots \infty = $

The sum of the series $\frac{2}{2 !} + \frac{2+4}{3 !} + \frac{2+4+6}{4 !} + \ldots$ is equal to

$1 + \frac{1 + 2}{1!} + \frac{1 + 2 + 3}{2!} + \frac{1 + 2 + 3 + 4}{3!} + \dots \infty = $

The sum of the series $\frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} - \dots$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module