Prove that 1/2 * 3/4 ***99/100 > 1/15

[Math Tutor]

Prove that:
[tex]\frac{1}{2}*\frac{3}{4}*\frac{5}{6}*\frac{7}{8}***\frac{99}{100}>\frac{1}{15}[/tex]

[Guest]

Do you want me to post it or we just let it to the new comers to solve it? Well, in order
to know that I solved it`ll give a clue according to my way: we get 15 > 10*sqrt(2) that is
1/(10*sqrt(2)) > 1/15.

Y0uRShAD0W (or we use a certain formula and prove it by induction)

[Guest]

Oh, there is also a third way that uses the logarithm and the fact that Sum_{1,n} 1/k > ln(n).

YS.