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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 26, 2020

Best Answer 

 #1
avatar+21017 
+1

Notice that the 3 of the first fraction cancels the three of the second fraction;

           that the 4 of the second fraction cancels the four of the third fraction;

           that the 5 of the third fraction cancels the five of the fourth fraction;

           etc.

 

This means that the only numbers remaining on the left side is the first numerator of 2 and the last denominator of n + 1.

The equation now becomes:  2 / (n + 1)  =  1 / 50

Cross-multiplying:                        (2)(50)  =  (1)(n + 1)

                                                         100  =  n + 1

                                                           99  =  n

 

The largest fraction on the left-hand side is:  99/100

 Mar 26, 2020
 #1
avatar+21017 
+1
Best Answer

Notice that the 3 of the first fraction cancels the three of the second fraction;

           that the 4 of the second fraction cancels the four of the third fraction;

           that the 5 of the third fraction cancels the five of the fourth fraction;

           etc.

 

This means that the only numbers remaining on the left side is the first numerator of 2 and the last denominator of n + 1.

The equation now becomes:  2 / (n + 1)  =  1 / 50

Cross-multiplying:                        (2)(50)  =  (1)(n + 1)

                                                         100  =  n + 1

                                                           99  =  n

 

The largest fraction on the left-hand side is:  99/100

geno3141 Mar 26, 2020

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