MathDB

Let

f(n)

be the sum of the first

n

terms of the sequence

0,1,1,2,2,3,3,4, \dots,

where the

n

th term is given by

a_n= \begin{cases} n/2 & \text{if } n \text{ is even,} \\ (n-1)/2 & \text{if } n \text{ is odd.} \end{cases}

Show that if

x

and

y

are positive integers and

x>y

then

xy=f(x+y)-f(x-y)

A1