the difference of the reciprocals of two successive integers equals the product of their reciprocals

Answer:
see below
Step-by-step explanation:
1 1
--- - --------
n n+1
Get a common denominator
1(n+1) 1(n)
---------- - --------
n(n+1) (n+1)n
n+1 - n
-----------------
n(n+1)
1
-----------------
n(n+1)
Separate into two fractions
1 1
---- * ------
n n+1