lim _{n rightarrow infty}left[frac{1}{n^2} se | vedclass

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Question

(D) આપેલ પદાવલિ $\lim _{n \rightarrow \infty}\left[\frac{1}{n^2} \sec ^2 \frac{1}{n^2}+\frac{2}{n^2} \sec ^2 \frac{4}{n^2}+\ldots+\frac{n}{n^2} \sec ^

Vedclass · Accepted Answer

$\frac{1}{2} 	an (1)$

Vedclass · Answer

(D) આપેલ પદાવલિ $\lim _{n ightarrow \infty}\left[\frac{1}{n^2} \sec ^2 \frac{1}{n^2}+\frac{2}{n^2} \sec ^2 \frac{4}{n^2}+\ldots+\frac{n}{n^2} \sec ^2 \frac{n^2}{n^2}ight]$ છે.આને $\int_0^1 x \sec^2(x^2) dx$ તરીકે લખી શકાય.ધારો કે $x^2 = t$,તેથી $2x dx = dt$,એટલે કે $x dx = \frac{1}{2} dt$.જ્યારે $x=0, t=0$ અને જ્યારે $x=1, t=1$.સંકલન $\frac{1}{2} \int_0^1 \sec^2 t dt = \frac{1}{2} [	an t]_0^1 = \frac{1}{2} 	an(1)$ થાય છે.

$\lim _{n \rightarrow \infty}\left[\frac{1}{n^2} \sec ^2 \frac{1}{n^2}+\frac{2}{n^2} \sec ^2 \frac{4}{n^2}+\ldots+\frac{1}{n} \sec ^2 1\right]=$

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