Unit fractions/Sum n+1 to 2n/ln 2/Hint/Exercise

Show that for every ${}n\in \mathbb {N} _{+}$ the estimate

${}{\frac {1}{n+1}}+{\frac {1}{n+2}}+\cdots +{\frac {1}{2n}}\leq \ln 2\,$

holds. Hint: Consider the function ${}f(x)={\frac {1}{x}}$ on the interval ${}[1,2]$.

Create a solution