Answer :

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


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