Question

find the sum of n terms of. ....

Answer 1

3 x 1^2 + 5 x 3^2 + 7 x 5^2 +......

here we use the concept of sigma

sigma (2r+1)(2r-1)^2

sigma (2r-1)(4r^2-4r+1)

sigma {8r^3-8r^2+2r-4r^2+4r-1}

sigma {8r^3-12r^2+6r-1}

8.sigma r^3 -12. sigma r^2 +6sigma. r -sigma 1.

8{n(n+1)/2}^2 -12n(n+1)(2n+1)/6 +6n(n+1)/2-n