lim _{x rightarrow 1} frac{x+x^2+ldots+x^n-n} | vedclass

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Question

(C) આપેલ લક્ષ $L = \lim _{x \rightarrow 1} \frac{x+x^2+\ldots+x^n-n}{x-1}$ છે.અંશને $(x-1) + (x^2-1) + \ldots + (x^n-1)$ તરીકે લખી શકાય.તેથી,$L = \lim

Vedclass · Accepted Answer

$\frac{n(n+1)}{2}$

Vedclass · Answer

(C) આપેલ લક્ષ $L = \lim _{x \rightarrow 1} \frac{x+x^2+\ldots+x^n-n}{x-1}$ છે.અંશને $(x-1) + (x^2-1) + \ldots + (x^n-1)$ તરીકે લખી શકાય.તેથી,$L = \lim _{x \rightarrow 1} \left( \frac{x-1}{x-1} + \frac{x^2-1}{x-1} + \ldots + \frac{x^n-1}{x-1} \right)$.પ્રમાણિત લક્ષ $\lim _{x \rightarrow a} \frac{x^n-a^n}{x-a} = na^{n-1}$ નો ઉપયોગ કરતા,દરેક પદ $k$ થશે.તેથી,$L = 1 + 2 + 3 + \ldots + n = \frac{n(n+1)}{2}$.

$\lim _{x \rightarrow 1} \frac{x+x^2+\ldots+x^n-n}{x-1}$ ની કિંમત શોધો.

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જો $a = \lim_{n \rightarrow \infty} \frac{1+2+3+\ldots+n}{n^2}$ અને $b = \lim_{n \rightarrow \infty} \frac{1^2+2^2+3^2+\ldots+n^2}{n^3}$ હોય,તો

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