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Simplify (1+3+5+...+199)/(2+4+6+...+198+200+202).

 Apr 20, 2022
 #1
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Sum of 1st n odds  =  n^2  ......we  have   [ 199 + 1 ]  / 2   =  100  odds

 

Sum of first evens =    [ first even + last even ] * n  / 2 

We have  202 / 2 = 101 evens

So  [ 204] * [101] / 2  =   even sum =  101 * 101

 

So

 

sum of odds  /sum of evens   =

 

100^2   / [ 102 * 101 ]  =

 

5000 /5151

 

 

cool cool cool

 Apr 20, 2022

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