It is required to find the sum 11² + 12² + 13²+ …20²

11² + 12² + 13²+ …20² = Sum of squares of natural numbers starting from 1 to 20 – Sum of squares of natural numbers starting from 1 to 10.

Note:

Sum of squares of first n natural numbers, 1² + 2² + 3²+….n²,

From the above identities,

Sum of squares of natural numbers starting from 1 to 20

Sum of squares of natural numbers starting from 1 to 10

11² + 12² + 13²+ …20²= Sum of squares of natural numbers starting from 1 to 20 – Sum of squares of natural numbers starting from 1 to 10.

11² + 12² + 13²+ …20² = 2870 – 385 = 2485