JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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{e^{x - 1 - \frac{1}{2}{{\left( {x - 1} \right)}^2} + \frac{1}{3}{{\left( {x - 1} \right)}^3} - \frac{1}{4}{{\left( {x - 1} \right)}^4} + \ldots }}

is equal to

View answer and explanation

Correct option: C

x

Option C is correct because the exponent simplifies to log(x) using the Taylor series expansion of log(1+x), and e^(log(x)) equals x.

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