Find the limit: _ x -1 [1+x+x^ 2 + +x^ 10 ] - Vidyadip

Question

Find the limit: $\lim \limits_{x \rightarrow-1}\left[1+x+x^{2}+\ldots+x^{10}\right]$

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Answer

$\lim \limits_{x \rightarrow-1}\left[1+x+x^{2}+\ldots+x^{10}\right]$ $=1+(-1)+(-1)^{2}+\ldots+(-1)^{10}$

= 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 = 1

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