frac{1}{2} + frac{1}{4} + frac{1}{8 times 2!} | vedclass

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

Question

(C) The given series is $S = \frac{1}{2} + \frac{1}{4} + \frac{1}{8 	imes 2!} + \frac{1}{16 	imes 3!} + \frac{1}{32 	imes 4!} + \dots \infty$. We c

Vedclass · Accepted Answer

$\frac{\sqrt{e}}{2}$

Vedclass · Answer

(C) The given series is $S = \frac{1}{2} + \frac{1}{4} + \frac{1}{8 	imes 2!} + \frac{1}{16 	imes 3!} + \frac{1}{32 	imes 4!} + \dots \infty$. We can rewrite this as $S = \frac{1}{2} \left[ 1 + \frac{1}{2} + \frac{1}{2^2 	imes 2!} + \frac{1}{2^3 	imes 3!} + \dots \infty ight]$. This is equivalent to $S = \frac{1}{2} \left[ 1 + \frac{(1/2)^1}{1!} + \frac{(1/2)^2}{2!} + \frac{(1/2)^3}{3!} + \dots \infty ight]$. Using the exponential series formula $e^x = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots \infty$,we substitute $x = \frac{1}{2}$. Thus,$S = \frac{1}{2} e^{1/2} = \frac{\sqrt{e}}{2}$.

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

Similar Questions

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

The money invested in a company is compounded continuously. ₹ $400$ invested today becomes ₹ $800$ in $6$ years. What will it become at the end of $33$ years? (Given $\sqrt{2} \approx 1.4142$)

Let $C(\theta) = \sum_{n=0}^{\infty} \frac{\cos(n\theta)}{n!}$. Which of the following statements is $FALSE$?

The sum $1+\frac{1+3}{2!}+\frac{1+3+5}{3!}+\frac{1+3+5+7}{4!}+\ldots$ up to $\infty$ terms is equal to (in $e$)

$\frac{1}{1!} + \frac{4}{2!} + \frac{7}{3!} + \frac{10}{4!} + \dots \infty = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module