Is this limit related to the harmonic series?

Calculus Level 3

A=limn(1n+1+1n+2++12n) A=\lim_{n\to\infty}{\left(\dfrac{1}{n+1}+\dfrac{1}{n+2}+\cdots+\dfrac{1}{2n} \right)}

Find the exact value of eAe^A if the limit exists, otherwise enter 0 as your answer.

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