A) \[x=\]
B) \[{{e}^{a}}\]
C) \[\frac{e}{{{e}^{b/a}}}\]
D) \[\frac{e}{{{e}^{a/b}}}\]
Correct Answer: C
Solution :
\[1+\frac{a-b}{a}+\frac{1}{2\ !}{{\left( \frac{a-b}{a} \right)}^{2}}\ +\frac{1}{3\ !}{{\left( \frac{a-b}{a} \right)}^{3}}+........\] \[=1+\frac{\left( \frac{a-b}{a} \right)}{1\ !}+\frac{{{\left( \frac{a-b}{a} \right)}^{2}}}{2\ !}+\frac{{{\left( \frac{a-b}{a} \right)}^{3}}}{3\ !}+.......\] \[={{e}^{(a-b)/a}}={{e}^{1-(b/a)}}={{e}^{1}}.{{e}^{-b/a}}=\frac{e}{{{e}^{b/a}}}\] .
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