Evaluate 1^2 + 2^2 + 3^2 + … + 10^2.

Given data

• Sum S = 1^2 + 2^2 + … + 10^2

Concept / Approach

• Use the formula: 1^2 + 2^2 + … + n^2 = n(n + 1)(2n + 1)/6

Step-by-step calculation

S = 10 × 11 × 21 / 6= (10 × 11 = 110); 110 × 21 = 23102310 ÷ 6 = 385

Verification

Manual partial sums (1^2+…+5^2 = 55; 6^2+…+10^2 = 330) ⇒ total 385.

Final Answer

Sum = 385.