Question

Lim x tends to infinity (x+1)^100

Answer 1

Step-by-step explanation:

We have,

$\lim_{x \rarr0} \frac{(x + 1) ^{100} + {(x + 2)}^{100} + ... + {(x + 100)}^{100} }{ {x}^{100} + {10}^{100} }$

$= \lim_{x \rarr0} \frac{ {x}^{100} \{(1 + \frac{1}{x} )^{100} + (1+ \frac{2}{x})^{100} + .... + ( 1 + \frac{100}{x} )^{100} \} }{ {x}^{100} (1 +( \frac{10}{x} ) ^{100}) }$

$= 100$