+0  
 
+1
90
3
avatar+40 

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 \(b\)?

hatchet288  Jun 28, 2018
 #1
avatar+3282 
+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

tertre  Jun 28, 2018
 #2
avatar+91297 
+1

Nice, tertre  !!!

 

 

cool cool cool

CPhill  Jun 28, 2018
 #3
avatar+3282 
+1

Thank you, CPhill!

smileysmiley

tertre  Jun 28, 2018

7 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.