Value of the value of the product

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sarasoleja

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Apr 4, 2011
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When exactly is the value of the value of the product equal (1+1/2)(1+1/3)(1+1/4)....(1+1/n) equal to an integer?

I don't know exactly what they're asking for, but the answer is when n is odd.

What tactic should be used to solve this question?

I would really appreciate ur help!
 
sarasoleja said:
When exactly is the value of the value of the product equal (1+1/2)(1+1/3)(1+1/4)....(1+1/n) equal to an integer?

I don't know exactly what they're asking for, but the answer is when n is odd.

What tactic should be used to solve this question?

I would really appreciate ur help!
Click to expand...

I think that is a typo!

Since first term has 2 in denominator - all other terms factor out - the numerator of the last term (n+1) must be even. (n+1) is even when 'n' is odd.

for example - expanding couple of terms:

\(\displaystyle \left(\frac{3}{2}\right ) \left(\frac{4}{3}\right ) \left(\frac{5}{4}\right ) \left(\frac{6}{5}\right ) \left(\frac{7}{6}\right )\)
 
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