Question

${lim}_{x\to 1}\frac{x^n-1}{x-1}$ is equal to

• A. $\frac{n}{2}$
• B. $\frac{n(n+1)}{2}$
• C. $n$
• D. $noneofthese$

Answer 1

The correct option is C $n$

${lim}_{x\to 1}\frac{x^n-1}{x-1}$

$={lim}_{x\to 1}\frac{(x-1)(x^{n-1}+x^{n-2}+.....+x+1)}{x-1}$

$={lim}_{x\to 1}\sum _{i=0}^{n-1}{x}^i$

$=\sum _{i=0}^{n-1}{1}^i$

$=\sum _{i=0}^{n-1}1$

$=n$

Hence, this is the answer.