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Recent questions tagged taylor-series

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GATE ECE 2015 Set 3 | Question: 5
The value of $\displaystyle{}\sum_{n=0}^{\infty} n \left(\dfrac{1}{2}\right)^{n}$ is ________.
The value of $\displaystyle{}\sum_{n=0}^{\infty} n \left(\dfrac{1}{2}\right)^{n}$ is ________.
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GATE ECE 2014 Set 4 | Question: 1
The series $\Sigma_{n=0}^{\infty} \frac{1}{n!}$ converges to $2 \text{ ln } 2$ $\sqrt{2}$ $2$ $e$
The series $\Sigma_{n=0}^{\infty} \frac{1}{n!}$ converges to$2 \text{ ln } 2$$\sqrt{2}$$2$$e$
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GATE ECE 2014 Set 1 | Question: 26
The Taylor series expansion of $3\sin x + 2 \cos x$ is $2 + 3x-x^{2} – \frac{x^{3}}{2} + \dots$ $2 – 3x + x^{2} – \frac{x^{3}}{2} + \dots$ $2 + 3x + x^{2} + \frac{x^{3}}{2} + \dots$ $2 – 3x – x^{2} + \frac{x^{3}}{2} + \dots$
The Taylor series expansion of $3\sin x + 2 \cos x$ is$2 + 3x-x^{2} – \frac{x^{3}}{2} + \dots$$2 – 3x + x^{2} – \frac{x^{3}}{2} + \dots$$2 + 3x + x^{2} + \frac...
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GATE ECE 2018 | Question: 24
Taylor series expansion of $f\left ( x \right )=\int ^{x}_{0}e^{-\left ( \frac{t^{2}}{2} \right )}dt$ around $x=0$ has the form $f\left ( x \right )={a}_{0}+a_{1}x+a_{2}x^{2}+...$ The coefficient $a_{2}$ (correct to two decimal places) is equal to ________.
Taylor series expansion of $f\left ( x \right )=\int ^{x}_{0}e^{-\left ( \frac{t^{2}}{2} \right )}dt$ around $x=0$ has the form $$f\left ( x \right )={a}_{0}+a_{1}x+a_{2}...
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