AP EAMCET · Maths · Limits
\(\lim _{x \rightarrow 1}\left(\frac{x+x^2+x^3+\ldots+x^n-n}{x-1}\right)=\)
- A \(\frac{n(n+1)}{2}\)
- B \(\frac{n+1}{2}\)
- C \(\frac{2}{n}\)
- D \(n\)
Answer & Solution
Correct Answer
(A) \(\frac{n(n+1)}{2}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } \lim _{x \rightarrow 1}\left(\frac{x+x^2+x^3 \ldots . x^4-n}{(x-1)}\right) \\ & =\lim _{x \rightarrow 1}\left(\frac{(x-1)+\left(x^2-1\right)+\left(x^3-1\right) \ldots+\left(x^n-1\right)}{(x-1)}\right) \\ & =\lim _{x \rightarrow 1}\left(1+2 x+3 x^2+4…
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