Question
What is the ratio of the sum of the squares of the first
8 natural numbers to the sum of the first 12 odd natural numbers?Solution
Sum of first 'n' odd numbers = n2
Sum of square of first 'n' natural numbers. =Â {(n x (n + 1) x (2n + 1)}/6
ATQ
Sum of square of first 8 natural numbers = {8 X ([8 + 1) X (8 X 2 + 1) ] ÷ 6} = [(8 X 9 X 17) ÷ 6] = 204
Sum of first 12 odd natural numbers = n2Â = 122Â = 144
Required ratio = (204/144) = 17:12
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