Correct option (a) n( 2n2 + 2n + 1)
Explanation:
S = n2 + 1 + n2 + 2 +… + n2 + 2n = 2n3 + n(2n + 1) = n(2n2 + 2n + 1)
Alternative Method: Suppose n = 2 then 1st term of the series will be 22 + 1 = 5. Now we want to find the sum of first 2n = 4 terms. First 4 terms of the series will be 5, 6, 7, 8. Sum = 26. If we put n = 2 in the above options then only option (a) satisfies.