+0  
 
+1
156
3
avatar+50 

If the product \(\frac{3}{2}*\frac{4}{3}*\frac{5}{4}*\frac{6}{5}*...*\frac{a}{b}=9\), what is the sum of \(a\) and \(b\)?

 Jun 28, 2018
 #1
avatar+3998 
+3

  By scanning the numerator and the denominator, we can see common numbers. So, 3 gets cancels out, 4, 5, 6, up to b, an unknown number. After all these cancelations, we are left with \(\frac{a}{2}=9\). This means that a, is \(9*2=18\). To find b, we look at our previous fractions, noting that the denominator is one less than the numerator, so that leaves us with: \(b=17\).

Thus, the answer is \(18+17=\boxed{35}\).

smileysmiley

 Jun 28, 2018
 #2
avatar+98197 
+1

Nice, tertre  !!!

 

 

cool cool cool

CPhill  Jun 28, 2018
 #3
avatar+3998 
+1

Thank you, CPhill!

smileysmiley

tertre  Jun 28, 2018

24 Online Users

avatar
avatar
avatar