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If \(e^{x} = 1 + x + \frac{x^{2}}{1.2} + \frac{x^{3}}{1.2.3}...

If $e^{x} = 1 + x + \frac{x^{2}}{1.2} + \frac{x^{3}}{1.2.3} + ...$ , find $\frac{1}{e^{\frac{1}{2}}}$

A.

1 - $\frac{x}{2}$ + $\frac{x^2}{1.2^3}$ + $\frac{x^3}{2^4.3}$ + .........

B.

1 - $\frac{x}{2}$ + $\frac{x^2}{1.2^3}$ + $\frac{x^4}{2.4.3}$ + ..

C.

1 + $\frac{x}{2}$ + $\frac{x^2}{1.2}$ + $\frac{x^3}{1.2.3}$ + $\frac{x^4}{1.23.4}$ + .........

D.

1 - x + $\frac{x^2}{1.2^3}$ + $\frac{x^3}{2^4.3}$ + .........

E.

1 + $\frac{x}{2}$ + $\frac{x^2}{1.2^3}$ + $\frac{x^4}{1.2.6}$ + .........

View answer & explanation

Correct answer is C

$e^{x} = 1 + x + \frac{x^{2}}{1.2} + \frac{x^{3}}{1.2.3} + ...$

$\frac{1}{e^{\frac{1}{2}}} = e^{-\frac{1}{2}}$

$e^{-\frac{1}{2}} = 1 - \frac{x}{2} + \frac{x^{2}}{1.2^{3}} - \frac{x^{3}}{1.2^{4}.3} + ...$

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