[Solved] How to get summation of i ∈∑ nCr where ( a

Use the hockey stick rule

bCr + (b-1)Cr + (b-2)Cr + .... + aCr =
bCr + (b-1)Cr + (b-2)Cr + .... + rCr - ((a-1)Cr+(a-2)Cr+...+rCr) =
(b+1)C(r+1)-aC(r+1)

For example, 6+10+15=4C2+5C2+6C2=7C3-4C3=35-4