Question

Prove: The difference of the reciprocals
of two successive integers equals the
product of their reciprocals.
1
1
-
n
n + 1
[?]
n(n + 1)
[ ].[
n n+1

Answer 1

Step-by-step explanation:

let two successive integers n, n+1

difference of the reciprocals:

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