WBJEE · Maths · Limits
The value of \(\lim _{x \rightarrow 1} \frac{x+x^2+\ldots+x^n-n}{x-1}\) is
- A \(\mathrm{n}\)
- B \(\frac{\mathrm{n}+1}{2}\)
- C \(\frac{\mathrm{n}(\mathrm{n}+1)}{2}\)
- D \(\frac{\mathrm{n}(\mathrm{n}-1)}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{\mathrm{n}(\mathrm{n}+1)}{2}\)
Step-by-step Solution
Detailed explanation
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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