Sum to n terms of the series

3.7.11.13 + 7.11.15.19 + 11.15.19.21 + ...

This question can definitely be solved using the V_n method.

S = Σ(4r-1)(4r+3)(4r+7)(4r+11), r=1,2,3,....n.

So T_r = (4r-1)(4r+3)(4r+7)(4r+11)

and let V_r = (4r-5)(4r-1)(4r+3)(4r+7)(4r+11)

hence, V_r+1 = (4r-1)(4r+3)(4r+7)(4r+11)(4r+15)

So V_r+1 - V_r = 20xT_r.

Hence Σ(V_r+1 - V_r) = 20*S

Hence S = (1/20)*[Vn+1 - V1] = (1/20)*[(4n-1)(4n+3)(4n+7)(4n+11)(4n+15) + 3.7.11.15] ------- (Required Answer)