Functions Question 325
Question: $ \underset{x\to \infty }{\mathop{\lim }},\frac{{{(x+1)}^{10}}+{{(x+2)}^{10}}+…..+{{(x+100)}^{10}}}{x^{10}+10^{10}} $ is equal to
Options:
A) 0
B) 1
C) 10
D) 100
Show Answer
Answer:
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}[ {{( 1+\frac{1}{x} )}^{10}}+{{( 1+\frac{2}{x} )}^{10}}+…+{{( 1+\frac{100}{x} )}^{10}} ]}{x^{10}[ 1+\frac{10^{10}}{x^{10}} ]}=100 $ .
BETA
