1^2 +2.2^2+3^3+2.2^4+5^2+5^2+2.6^2 ........ is n(n+1)^2/2 when "n" is even . What is the sum when n is odd?

When n is odd, last term will be n^2.

 

Thus, 

Sum = 1^2 +2.2^2+3^3+2.2^4+5^2+2.6^2 ... + 2.(n-1)^2 + n^2

= [(n-1)(n)^2]/2 + n^2      [Replacing n by (n - 1)]

= [n^3 + n^2]/ 2 = [n^2(n+1)]/2