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Question

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

1+xlog⁡ea+x22!(log⁡ea)2+x33!(log⁡ea)3+...=1 + x\log_{e}a + \frac{x^{2}}{2!}(\log_{e}a)^{2} + \frac{x^{3}}{3!}(\log_{e}a)^{3} + ... =

A

axa^{x}

B

x

C

alog⁡axa^{\log_{a}x}

D

a

Answer

axa^{x}

Explanation

Solution

Series

= 11.3+12.13.5+13.15.7+......∞=\frac{1}{1.3} + \frac{1}{2}.\frac{1}{3.5} + \frac{1}{3}.\frac{1}{5.7} + ......\infty =

2log⁡e2−12\log_{e}2 - 1.