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

 Mar 18, 2018
 #1
avatar+100588 
+2

Note  that 

1 + 3 + 5 + 7 +.......+ 199     has  100 terms

And the sum of these =  n^2  = 100^2  = 100 * 100

 

And  

2 + 4 + 6 + 8 + ......+ 200   also has  100 terms

And the sum of these  is  n(n + 1)   =  100 (101)

 

So

 

[  1 + 3 + 5 + 7 + ....+ 199 ]            100 * 100                  100

______________________  =  ___________   =          ___ 

[ 2 + 4 + 6 + 8 +......+ 200]             100 * 101                  101

 

 

 

cool cool cool

 Mar 18, 2018
edited by CPhill  Mar 19, 2018
 #2
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A slight typo !! Should be = 100 / 101

 Mar 18, 2018

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