Question

$\lim_{x \rightarrow \infty}\frac{(x + 1)^{10} + (x + 2)^{10} + ..... + (x + 100)^{10}}{x^{10} + 10^{10}}$is equal to

• A. 0
• B. 1
• C. 10
• D. 100

Answer 1

Answer: (D)

100

Answer 2

$\lim _ { x \rightarrow \infty } \frac { ( x + 1 ) ^ { 10 } + ( x + 2 ) ^ { 10 } + \ldots \ldots + ( x + 100 ) ^ { 10 } } { x ^ { 10 } + 10 ^ { 10 } }$

$= \lim_{x \rightarrow \infty}\frac{x^{10}\left\lbrack \left( 1 + \frac{1}{x} \right)^{10} + \left( 1 + \frac{2}{x} \right)^{10} + ... + \left( 1 + \frac{100}{x} \right)^{10} \right\rbrack}{x^{10}\left\lbrack 1 + \frac{10^{10}}{x^{10}} \right\rbrack} = 100$.