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Previous Year Question (PYQs)

$\displaystyle \lim_{x\to1}\frac{x+x^{2}+\ldots+x^{10}-10}{5x-5}$ is equal to …




Solution

Let $f(x)=x+x^{2}+\ldots+x^{10}-10$. Then $f'(x)=1+2x+3x^{2}+\ldots+10x^{9}$. At $x=1$, $f'(1)=1+2+3+\ldots+10=55$. Hence limit $=\dfrac{f'(1)}{5}=\dfrac{55}{5}=11$.

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