Simplify(1+3+5+...+199)/(2+4+6+...+200)

We have  [ 199 -1] / 2  + 1  =  100 terms at the top

And  the sum of the terms at the top can be written as

( 1 + 199) (100) / 2   =    200 * 100 /2  =  200 * 50

And we have  [ 200 - 2 ] / 2  +1     =  198/2 +  1   =  99 + 1  = 100 terms on the bottom

And the sum of these terms is    ( 200 + 2) (100/2)  =  202 * 50

So we have

[  200 * 50  ] / [ 202 * 50]  =  200 / 202  =   100 / 101