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Question

Question: \[\left( \frac{a - b}{a} \right) + \frac{1}{2}\left( \frac{a - b}{a} \right)^{2} + \frac{1}{3}\left(...

(aba)+12(aba)2+13(aba)3+.....=\left( \frac{a - b}{a} \right) + \frac{1}{2}\left( \frac{a - b}{a} \right)^{2} + \frac{1}{3}\left( \frac{a - b}{a} \right)^{3} + ..... =

A

loge(ab)\log_{e}(a - b)

B

loge(ab)\log_{e}\left( \frac{a}{b} \right)

C

loge(ba)\log_{e}\left( \frac{b}{a} \right)

D

e(aba)e^{\left( \frac{a - b}{a} \right)}

Answer

loge(ab)\log_{e}\left( \frac{a}{b} \right)

Explanation

Solution

loge(1+y)\log_{e}(1 + y)

e5x+exe3x\frac{e^{5x} + e^{x}}{e^{3x}}.