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Consider this pattern where the positive, proper fractions with denominator (n+1) are arranged in the nth row in a triangular formation. The 1st through 4th rows are shown; each row has one more entry than the previous row. What is the sum of the fractions in the 15th row?

 Sep 21, 2016
 #1
avatar+129852 
+2

Notice the progressive sums :   1/2, 1 , 3/2 , 2   =   1/2 + 2/2 + 3/2 + 4/2

 

So, it appears that the sum of the fractions in any row  "n' will be =    n/2

 

And in the 15th row the sum will be  :   15/2 =   7.5

 

 

 

cool cool cool

 Sep 21, 2016
 #2
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Cphill: Aren't the terms of the 15th row: 1/15, 2/15, 3/15...........14/15. The 15/15 not being considered a fraction but a whole number? So you have 14 terms: S=[1/15 +14/15] /2 x 14=7???.

 Sep 21, 2016
 #3
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Now, I get it!. The 15th row begins with: 1/16, 2/16.........15/16. You are right as always. My s***w-up!.

 Sep 21, 2016
 #4
avatar+129852 
+1

The 15th row  will have denominators of 16, not 15........and there will be 15 fractions, 1/16 to 15/16...so the sum will be

 

 ([ 15 *16] / 2 )  /  16    =     15 / 2   = 7.5 

 

 

 

 

 

cool cool cool

 Sep 21, 2016

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