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Question: \[\frac{1.2}{1!} + \frac{2.3}{2!} + \frac{3.4}{3!} + \frac{4.5}{4!} + .....\infty =\]...

1.21!+2.32!+3.43!+4.54!+.....∞=\frac{1.2}{1!} + \frac{2.3}{2!} + \frac{3.4}{3!} + \frac{4.5}{4!} + .....\infty =

A

2e2e

B

3e3e

C

3e−13e - 1

D

ee

Answer

3e3e

Explanation

Solution

e−xe^{- x},

Hereee

ex21+1+x2!+1+x+x23!+1+x+x2+x34!+.....∞=e^{x^{2}}1 + \frac{1 + x}{2!} + \frac{1 + x + x^{2}}{3!} + \frac{1 + x + x^{2} + x^{3}}{4!} + .....\infty =.