The value of $\lim _{x \rightarrow 1} \frac{x+x^2+\ldots+x^n-n}{x-1}$ is

Question

The value of $\lim _{x \rightarrow 1} \frac{x+x^2+\ldots+x^n-n}{x-1}$ is, $\mathrm{n}$, $\frac{\mathrm{n}+1}{2}$, $\frac{\mathrm{n}(\mathrm{n}+1)}{2}$, $\frac{\mathrm{n}(\mathrm{n}-1)}{2}$

MARKS App · Accepted Answer

Hints: $\operatorname{Lt}_{x \rightarrow 1} \frac{(x-1)+\left(x^2-1\right)+\left(x^3-1\right) \ldots \ldots \ldots \ldots .\left(x^4-1\right)}{x-1}$ $=1+2+3 \ldots \ldots \ldots \ldots \ldots \ldots+n=\frac{\mathrm{n}(\mathrm{n}+1)}{2}$

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