Question

The values of $\underset{x\to 1}{lim}\frac{x+x^2+....x^n-n}{x-1}$

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

Answer 1

The correct option is C $\frac{n(n+1)}{2}$

put $x=1$ we get undetermined values

so apply L'hospital rule

now numerator is $1+2x+3x^2+4x^3+.......$

denominator is $1$

now apply limit $x=1$

$1+2+3+4+.....+n=\frac{n(n+1)}{2}$