Simplify (1+3+5+...+199)/(2+4+6+...+198+200+202).
The numerator: [199 - 1] / 2 + 1==100>>>> n^2==100^2==10,000
The denominator: [202 - 2] / 2 + 1==101>>>> n(n+1)=101*102==10,302
10,000 / 10,302==5000 / 5151
