limx→1 ∑r=1n xr−nx−1is equal to - Infinity Learn by Sri Chaitanya

A
$\frac{n}{x}$
B
$\frac{n (n + 1)}{2}$
C
$1$
D
$0$

Solution:

we have,

$\begin{array}{l} lim_{x \to 1} \frac{\sum^{n} x^{n} - n}{x = 1} = lim_{x \to 1} \frac{x - 1}{x - 1} + \frac{x^{2} - 1^{2}}{x - 1} + \frac{x^{3} - 1^{3}}{x - 1} + \dots + \frac{x^{n} - 1^{n}}{x - 1} \\ = 1 + 2 + 3 + \dots + n = \frac{n (n + 1)}{2} \end{array}$

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