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

Explanation:

let two successive integers n, n+1

difference of the reciprocals:

`(1)/(n)-(1)/(n+1) \\=((n+1)-n)/((n)(n+1))\\=(1)/((n)(n+1))\\=(1)/((n))(1)/((n+1))\\`