Look at some simple examples, with, say, T= 3. The outer sum then goes t= 1, t= 2, t= 3: for each such t, the term being added is

t= 1)

t= 2)

t= 3)

(Adding "1" from y= 1 to t just gives "t")

That entire sum is .

On the right side, again with T= 3, y takes on values of 1, 2, 3 and the inner sum there is

y= 1)

y= 2)

y= 3)

Multiplying each of those by "1" and adding gives , exactly the same.

For any T, both right and left hand sides give .