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1 solution
sum of all squares from 1 to n(terms) =n(n+1)(2n+1) / 6
sum of all odd squares from 1 to n(terms) = n(2n+1)(2n-1) / 3
Yellow Area = pi 1^2 + pi 3^2 - pi2^2 + pi 5^2 - pi 4^2 .......+pi 99^2 - pi 98^2
similarly
Green Area = pi * ( 2^2 - 1^2 + 4^2 - 3^2 + 6^2 - 5^2.........100^2 - 99^2)
ratio = pi [ 1 + ( 9 - 4) + ( 25-16) + ( 49 -36) .....(98 +99) ] / pi * [( 4 -1) + (16-9) + (36 -25) + ( 64 -49) .......(100+99) ]
= [1 + 5 + 9 ..... + 197 ] / [3 + 7 + 11 ... + 199]
= 99/101