Let
Compute:
Thanks in advance!
Notice that
So 10 out of your 100 terms give f(1)
and
5 of these terms give f(0.5) and 5 more give f(2).
Already, we have regrouped 20 out of 100 of these terms in 3 simple operations: 10f(1)+5f(0.5)+5f(2).
I suspect the 80 remaining could also be regrouped like this!