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Question: \[\log_{e}\frac{4}{5} + \frac{1}{4} - \frac{1}{2}\left( \frac{1}{4} \right)^{2} + \frac{1}{3}\left( ...

log⁡e45+14−12(14)2+13(14)3+.....\log_{e}\frac{4}{5} + \frac{1}{4} - \frac{1}{2}\left( \frac{1}{4} \right)^{2} + \frac{1}{3}\left( \frac{1}{4} \right)^{3} + .....

A

2log⁡e452\log_{e}\frac{4}{5}

B

log⁡e54\log_{e}\frac{5}{4}

C

1

D

0

Answer

0

Explanation

Solution

1+a−bx1!+(a−bx)22!+(a−bx)33!+....∞=1 + \frac{a - bx}{1!} + \frac{(a - bx)^{2}}{2!} + \frac{(a - bx)^{3}}{3!} + ....\infty =

= ea−bxe^{a - bx}.