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Question: \[\frac{2}{1!}\log_{e}2 + \frac{2^{2}}{2!}(\log_{e}2)^{2} + \frac{2^{3}}{3!}(\log_{e}2)^{3} + .....\...

21!log⁡e2+222!(log⁡e2)2+233!(log⁡e2)3+.....∞=\frac{2}{1!}\log_{e}2 + \frac{2^{2}}{2!}(\log_{e}2)^{2} + \frac{2^{3}}{3!}(\log_{e}2)^{3} + .....\infty =

A

2

B

3

C

4

D

None of these

Answer

3

Explanation

Solution

Sum = 2log⁡322\log_{3}2.