Prove that if m n N then sigmank 0 km k m m n 1 m 1 m

Prove that if m, n N, then sigma^n_k = 0 k(m + k m) = (m + n + 1 m + 1) - (m + n+ 1 m + 2).

Solution

Either some of the information is not provided. Or if the statement is complete, then this equality is not correct. So there is no point to prove it. Because LHS and RHS are not equal. You can check by taking n=1.

LHS becomes m+1 whereas EHS becomes 0

m -1