A calculus problem by Sambhrant Sachan

Calculus Level 3

\[ \displaystyle \lim_{n \to \infty} \left( \dfrac{1}{n+1}+\dfrac{1}{n+2}+\dfrac{1}{n+3}+\cdots+\dfrac{1}{n+10^{10^{100}}} \right) =\, ? \]


Inspiration.

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