Integration of Infinite Series<p></p>$\int {{{\left( {\frac{1}{{2!}} - \frac{1}{{3!}} + \frac{1}{{4!}} - \frac{1}{{5!}} + .........} \right)}^x}dx} = ?$

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Integration of Infinite Series
$\int {{{\left( {\frac{1}{{2!}} - \frac{1}{{3!}} + \frac{1}{{4!}} - \frac{1}{{5!}} + .........} \right)}^x}dx} = ?$

We have, ${e^{ - 1}} = 1 + ( - 1) + \frac{{{{( - 1)}^2}}}{{2!}} + \frac{{{{( - 1)}^3}}}{{3!}} + \frac{{{{( - 1)}^4}}}{{4!}} + ..........$

The given integral = $\int {{{({e^{ - 1}})}^x}dx} = \int {{e^{ - x}}dx} = - {e^{ - x}} + C$

Sum of the coefficients in the expansion of $(x+y)^n$ ....

If the sum of the coefficients in the expansion of $(x+y)^n$ is 4096, then the greatest coefficient in the expansion is _ _ _ _ . Solution $C_0 + C_1 + C_2 + C_3 + ......................... + C_n =4096 $ $\therefore 2^n = 4096 =2^{12} $ $\Rightarrow n = 12 $ Greatest coefficient = ${}^{12}{C_6} = 924$

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Integration of Infinite Series
$\int {{{\left( {\frac{1}{{2!}} - \frac{1}{{3!}} + \frac{1}{{4!}} - \frac{1}{{5!}} + .........} \right)}^x}dx} = ?$

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Sum of the coefficients in the expansion of $(x+y)^n$ ....

123IITJEE

Integration of Infinite Series$\int {{{\left( {\frac{1}{{2!}} - \frac{1}{{3!}} + \frac{1}{{4!}} - \frac{1}{{5!}} + .........} \right)}^x}dx} = ?$

Popular posts from this blog

Sum of the coefficients in the expansion of $(x+y)^n$ ....

Integration of Infinite Series
$\int {{{\left( {\frac{1}{{2!}} - \frac{1}{{3!}} + \frac{1}{{4!}} - \frac{1}{{5!}} + .........} \right)}^x}dx} = ?$