Show that the sequence ( a n ) n ∈ N {\displaystyle {}(a_{n})_{n\in \mathbb {N} }} with a n = 1 n + 1 + ⋯ + 1 2 n {\displaystyle {}a_{n}={\frac {1}{n+1}}+\cdots +{\frac {1}{2n}}}
with
