prove the inequality: 1/19 <(1/2).(4/5).(7/8).(10/11)....(2008/2009) < 1/12 i tr

Question

prove the inequality: 1/19 <(1/2).(4/5).(7/8).(10/11)....(2008/2009) < 1/12

i tried everything and still i can't prove it..I'm a good studentand that exercise is as a challenge..so any help i willappreciate..the second inequality is easier than first..i will bevery satisfied if you will prove only one from twoinequalities..thanks..

i tried the following: let L= (2/1).(5/4).(8/7)....(2009/2008)
so i have to prove that: 12<L<19
i will put function ln: lnL = ln(2/1) + ln(5/4) +ln(8/7)+..+ln(2009/2008)= ln(1+1) + ln(1+1/4) +ln(1+1/7)+...+ln(1+1/2008)
using now that: (1/n+1)< ln(1+1/n)<1/n (i will use only thesecond)
we have that lnL>(1/2)+(1/5)+(1/8)+..+(1/2009) and i have tofind a good approximation for the last one(let A) i don't know howand after just say that L>exp(A)..so i stuck here because isvery difficult to find such a good A to show that exp(A)>12..soplease help...you can use any way to solve it i don't matter frominequalities of university or whatever i will understand don'tworry, i already know too much so i want just somehow to proveit..(is important to find the solution without calculator but ifyou can't find a way to prove it without calculator let it be)

Explanation / Answer

(i.e. (1/2)*(4/5)*(7/8)....etc.)

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