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# Problem of the week, #5

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123
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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
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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 $$18+17=\boxed{35}$$.

Jun 28, 2018
#2
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Nice, tertre  !!!

CPhill  Jun 28, 2018
#3
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Thank you, CPhill!

tertre  Jun 28, 2018