The $10^{t h}$ term in the expansion of $e^{x}$ is

\frac{x^{10}}{10!}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{x^{9}}{9!}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{x^{9}}{10!}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x^{9}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $\frac{x^{9}}{9!}$
The exponential function is expanded as
$e^{x} = \infty \sum 0 \frac{x^{n}}{n!} = 1 + x + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} + \frac{x^{4}}{4!} + . . . .$
Therefore, the 10th term would be $\frac{x^{9}}{9!}$

Suggest Corrections

Similar questions

x^{10}

x^{9}

{(2 x^{2} - \frac{1}{x})}^{20}

x

{(x^{9} - \frac{1}{x})}^{9}

x

{(x^{2} + \frac{1}{x})}^{9}

x^{9}, x^{10}, x^{11}

(1 + x)^{n}

n^{2} - 41 n

x^{9}, x^{10}, x^{11}

{(1 + x)}^{n}

n^{2} - 41 n =

Join BYJU'S Learning Program