Let f(x)=x+x2+⋯+xn−nx−1,x≠1, the value of f1 of that f is continuous is

Let $f (x) = \frac{x + x^{2} + \dots + x^{n} - n}{x - 1}, x \neq 1,$ the value of $f (1)$ of that $f$ is continuous is

$f (1) = lim_{x \to 1} \frac{x + x^{2} + \dots + x^{n} - n}{x - 1} (\frac{0}{0} form)$

$= lim_{x \to 1} \frac{1 + 2 x + \dots + n x^{n - 1}}{1} = 1 + 2 + \dots + n$

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

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