JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Application +4 | -1

The coefficient of

{x^n}

in the series

1 + \frac{{a + bx}}{{1!}} + \frac{{{{\left( {a + bx} \right)}^2}}}{{2!}} + \frac{{{{\left( {a + bx} \right)}^3}}}{{3!}} = \ldots \infty

View answer and explanation

Correct option: C

{e^a}.\frac{{{b^n}}}{{n!}}

Option C (

{e^a}.\frac{{{b^n}}}{{n!}}

) is correct because the series represents the exponential function

e^{a+bx}

, and the coefficient of

x^n

can be found by expanding

e^{bx}

and multiplying by

e^a

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