Find the sum 112 + 122 + 132+ …202
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