Evaluate: 11^2 + 12^2 + 13^2 + ⋯ + 20^2.

Given data

• Sum of squares from 11 to 20.

Concept / Approach

• Use the closed form for 1^2 + 2^2 + ⋯ + n^2, then subtract 1^2 + ⋯ + 10^2.
• Formula: 1^2 + ⋯ + n^2 = n(n + 1)(2n + 1)/6.

Step-by-step calculation

Sum(1→20) = 20 × 21 × 41 / 620 × 21 = 420; 420 × 41 = 17,220; divide by 6 ⇒ 2,870Sum(1→10) = 10 × 11 × 21 / 6 = 385Required sum = 2,870 − 385 = 2,485

Verification

Spot-check: 20^2 = 400, 19^2 = 361, …; partial sums align with the computed total.

Common pitfalls

• Forgetting to subtract the first 10 squares.
• Arithmetic errors when multiplying 420 × 41.

Final Answer

2485