Question

Find the sum of the first 12 terms of the series \(1^2+2^2+3^2+4^2+\ldots\)

(A) 650
(B) 610
(C) 510
(D) 810

Answer 1

To find the sum of the first 12 terms of the square numbers series, use the formula n(n + 1)(2n + 1)/6. When n = 12, the sum equates to 650. So, the answer is (A) 650.

Step-by-step explanation:

The student is asking to find the sum of the first 12 terms of the square numbers series 12 + 22 + 32 + 42 + …. This series can be summed up using the formula for the sum of the squares of the first n natural numbers which is n(n + 1)(2n + 1)/6. For n = 12, the sum is 12(12 + 1)(24 + 1)/6, which calculates to 650.

Therefore, the correct answer is (A) 650.