What is the sum of the squares of first 20 even natural numbers?
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Given : squares of first 20 even natural numbers
To Find : Sum
Solution:
Sum= 2² + 4² + 6² + ______________ + 38² + 40²
=> Sum = 2² ( 1² + 2² + 3² + ____________ + 19² + 20²)
∑n² = n(n + 1) (2n + 1)/6
1² + 2² + 3² + ____________ + 19² + 20 = 20 (20 + 1)(2 * 20 + 1) / 6
= 20 * 21 * 41 / 6
= 2870
Sum = 2² (2870)
=> Sum = 4 (2870)
=> Sum = 11480
sum of the squares of first 20 even natural numbers = 11480
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