Find the sum

It is required to find the sum $11^{2}+12^{2}+13^{2}+\ldots 20^{2}$

$11^{2}+12^{2}+13^{2}+\ldots 20^{2}=$ 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, $1^{2}+2^{2}+3^{2}+\ldots n^{2}$

$\sum_{k=1}^{n} k^{2}=\frac{n(n+1)(2 n+1)}{6}$

From the above identities,

Sum of squares of natural numbers starting from 1 to 20

$=\frac{20(21)(41)}{6}=2870$

Sum of squares of natural numbers starting from 1 to 10

$=\frac{10(11)(21)}{6}=385$

$11^{2}+12^{2}+13^{2}+\ldots 20^{2}=$ Sum of squares of natural numbers starting from 1 to $20-$ Sum of squares of natural numbers starting from 1 to 10 .

$11^{2}+12^{2}+13^{2}+\ldots 20^{2}=2870-385=2485$