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Question

Question: \[1 + \frac{2^{2}}{1!} + \frac{3^{2}}{2!} + \frac{4^{2}}{3!} + ......\infty =\]...

1+221!+322!+423!+......=1 + \frac{2^{2}}{1!} + \frac{3^{2}}{2!} + \frac{4^{2}}{3!} + ......\infty =

A

2e2e

B

3e3e

C

(0.5)(0.5)22+(0.5)33(0.5)44+....(0.5) - \frac{(0.5)^{2}}{2} + \frac{(0.5)^{3}}{3} - \frac{(0.5)^{4}}{4} + ....

D

5e5e

Answer

5e5e

Explanation

Solution

x2y=2xyx^{2}y = 2x - y

Here x2y=2x+yx^{2}y = 2x + y

x=2y21x = 2y^{2} - 1

x2y=2x+y2x^{2}y = 2x + y^{2}.