Home

 Solve any problem (step by step solutions) Input table (Matrix, Statistics)
Mode :
SolutionHelp
 Solution Prove that 1 * 2^2 + 3 * 5^2 + 5 * 8^2 + ... n terms = n/2 (9n^3 + 4n^2 - 4n - 1)Solution:Your problem -> Prove that 1 * 2^2 + 3 * 5^2 + 5 * 8^2 + ... n terms = n/2 (9n^3 + 4n^2 - 4n - 1)L.H.S. = 1 × 2^2 + 3 × 5^2 + 5 × 8^2 + ... n terms= sum [ f(n) ]= sum [ (2n - 1)(3n - 1)^2 ]= sum [ (2n - 1)(9n^2 - 6n + 1)]= sum [ 18n^3 - 21n^2 + 8n - 1]= 18 sum n^3 - 21 sum n^2 + 8 sum n - sum 1= 18 * (n^2 (n+1)^2)/4 - 21 * (n (n + 1) (2n + 1))/6 + 8 * (n (n+1))/2 - n= n/2 [ 9 n (n + 1)^2 - 7(n + 1) (2n + 1) + 8 (n+1) - 2 ]= n/2 [ 9 n (n^2 + 2n +1) - 7 (2n^2 + 3n + 1) + 8 n + 8 - 2 ]= n/2 [ 9 n^3 + 18 n^2 + 9n - 14n^2 - 21n - 7 + 8 n + 8 - 2 ]= n/2 [ 9 n^3 + 4 n^2 - 4n - 1 ]= R.H.S. (Proved) Solution provided by AtoZmath.com Any wrong solution, solution improvement, feedback then Submit Here Want to know about AtoZmath.com and me