This is how I mentally solved it. Well, I used my fingers, also. 10^2 + (10 + 1)^2 + ... + (10 + 4)^2 taking into account (a + b)^2 = a^2 + 2ab + b^2, we have 10^2 appears 5 times: 500 the 2ab term gives: 2 * (10*1 + 10*2 + 10*3 + 10*4) = 20 * (1 + 2 + 3 + 4) = 200; 700, up to now then, the sum of the squares: 1^2 + 2^2 + 3^2 + 4^2 = 1 + 4 + 9 + 16 = 30. numerator sums 730. denominator: 350 + 15, times two gives 700 + 30; answer: 2