Question

Prove: The difference of the reciprocals

Answer 1

Step-by-step explanation:

let two successive integers n, n+1

difference of the reciprocals:

$\frac{1}{n}-\frac{1}{n+1} \\=\frac{(n+1)-n}{(n)(n+1)}\\=\frac{1}{(n)(n+1)}\\=\frac{1}{(n)}\frac{1}{(n+1)}$