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Simplify (1+3+5+...+199+201+203)/(2+4+6+...+200+202+204).

 Dec 9, 2021
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Sum formulas to the rescue! 

It is a formula that the sum of the first n odd numbers is n^2. There are (203+1)/2 = 102 odd numbers here, so our numerator is 102^2.

Our denominator is 2*(1+2+3+...+102), which, by the triangular number theorem, is 102(103). 

Thus, our answer is 102^2/(102*103) = 102/103

 Dec 9, 2021

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