Answer
$n \gt 10^{60}$
Work Step by Step
Since, we have $\int_n^\infty \dfrac{1}{x^{1.1}}dx \lt 0.00001$
or,$ \lim\limits_{a \to \infty} (\dfrac{-10}{a^{0.1}}+\dfrac{10}{n^{0.1}})\lt 0.00001$
or, $\dfrac{10}{n^{0.1}} \lt 0.00001 $
or, $n \gt (10^6)^{10}$
Hence, $n \gt 10^{60}$
