A) 0
B) 1
C) 10
D) 100
Correct Answer: D
Solution :
\[\underset{x\to \infty }{\mathop{\lim }}\,\frac{{{(x+1)}^{10}}+{{(x+2)}^{10}}+......+{{(x+100)}^{10}}}{{{x}^{10}}+{{10}^{10}}}\] \[=\underset{x\to \infty }{\mathop{\lim }}\,\frac{{{x}^{10}}\left[ {{\left( 1+\frac{1}{x} \right)}^{10}}+{{\left( 1+\frac{2}{x} \right)}^{10}}+...+{{\left( 1+\frac{100}{x} \right)}^{10}} \right]}{{{x}^{10}}\left[ 1+\frac{{{10}^{10}}}{{{x}^{10}}} \right]}=100\].
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