lim _{n rightarrow infty} frac{1^{77}+2^{77}+ | vedclass

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Question

(D) આપેલ લક્ષ: $\lim _{n \rightarrow \infty} \frac{1^{77}+2^{77}+\ldots+n^{77}}{n^{78}}$આને આ રીતે લખી શકાય: $\lim _{n \rightarrow \infty} \frac{1}{n}

Vedclass · Accepted Answer

$\frac{1}{78}$

Vedclass · Answer

(D) આપેલ લક્ષ: $\lim _{n \rightarrow \infty} \frac{1^{77}+2^{77}+\ldots+n^{77}}{n^{78}}$આને આ રીતે લખી શકાય: $\lim _{n \rightarrow \infty} \frac{1}{n} \sum_{r=1}^{n} \left(\frac{r}{n}\right)^{77}$નિશ્ચિત સંકલનની વ્યાખ્યા મુજબ,$\lim _{n \rightarrow \infty} \frac{1}{n} \sum_{r=1}^{n} f\left(\frac{r}{n}\right) = \int_{0}^{1} f(x) dx$અહીં,$f(x) = x^{77}$.તેથી,લક્ષનું મૂલ્ય: $\int_{0}^{1} x^{77} dx$સંકલન કરતા: $\left[ \frac{x^{78}}{78} \right]_{0}^{1} = \frac{1^{78}}{78} - \frac{0^{78}}{78} = \frac{1}{78}$

$\lim _{n \rightarrow \infty} \frac{1^{77}+2^{77}+\ldots+n^{77}}{n^{78}} = $

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