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If ,\(\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot...\cdot\frac{n}{n+1} = \frac{1}{50}\) what is the sum of the numerator and denominator of the largest fraction on the left side of the equation?

 Mar 27, 2020
 #1
avatar+111321 
+1

Note   that  in all the  fractions, the  denominator  of the  previous fraction will "cancel"  the  numerator  of the  next

 

So   at the end  we  will   have  this left

 

      2                  1

_______  =        ___      cross-multiply

  n +  1                50

 

50 (2)  =  1 ( n + 1)

 

100 =   n + 1       subtract  1  from both sides

 

99   =  n

 

n + 1  =  100

 

So....the  sum   of  n , n + 1  =    199

 

 

cool cool cool

 Mar 27, 2020
 #2
avatar+1956 
+1

Chris!! You beat me to it!!!

CalTheGreat  Mar 27, 2020
 #4
avatar+111321 
0

LOL!!!!....sorry, Cal    !!!!!

 

 

cool cool cool

CPhill  Mar 27, 2020
 #3
avatar+1956 
+1

Here is another answer, even though I'm not one of the "awesome people>"

 

Since all of these cross out, we're left with

 

2/(n+1)=1/50.

 

Therefore, the number has to be 1/100, making n+1 100.

Therefore, n=100,

100+99=199.

 

Hope this helped!

 Mar 27, 2020

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