Question 151
Let
$$S=\frac1n+\frac1{n+1}+\cdots+\frac1{n+m},\qquad n,m\in\{1,2,3,\ldots\}.$$
a) Prove that $S$ cannot be a natural number.
b) For $m=2(n-1)$, find, with justification, $k\in\mathbb N$ such that $k\lt S\lt k+1$.
$$S=\frac1n+\frac1{n+1}+\cdots+\frac1{n+m},\qquad n,m\in\{1,2,3,\ldots\}.$$
a) Prove that $S$ cannot be a natural number.
b) For $m=2(n-1)$, find, with justification, $k\in\mathbb N$ such that $k\lt S\lt k+1$.