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Bound the product (Posted on 2015-02-13) Difficulty: 2 of 5
Let
pr=(1/2)*(3/4)*(5/6)... *(99/100)

Without explicit computation prove that
pr is less than 1/10, but more than 1/15.

No Solution Yet Submitted by Ady TZIDON    
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re: Possible solution. Correction and second part. | Comment 3 of 4 |
(In reply to Possible solution. by broll)

Your ps has only 49 terms.  But if you add (100/101) the proof becomes a little stronger: (pr)^2<1/101


for pq use 1/2*2/3*4/5*6/7*...100/101
which is less than pr

pq*pr = 1/2*1/101 = 1/202
pr^2 > 1/202
pr > 1/sqrt(202) > 1/15

  Posted by Jer on 2015-02-13 12:47:18
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