Infinite product of consecutive odd/even, even/odd ratiosby Loren Booda Tags: consecutive, even or odd, infinite, odd or even, product, ratios 

#1
Sep1609, 05:16 PM

P: 3,408

[tex]?=\prod_{n=1}^\infty(n/(n+1))[/tex]




#2
Sep1609, 05:35 PM

Sci Advisor
HW Helper
P: 3,680

Let
[tex]P(N)=\prod_{n=1}^N\frac{n}{n+1}.[/tex] Then you're looking for [itex]\lim_{n\to\infty}P(n).[/itex] P(1) = 1/2, P(2) = 1/2 * 2/3 = 1/3, P(3) = ... do you see what's going on here? What's the limit going to be? 



#3
Sep1609, 07:52 PM

P: 7

[tex]\lim_{N \to \infty}P(N) = \lim_{N \to \infty} \frac{1}{N+1} = 0.[/tex]



Register to reply 
Related Discussions  
Product of r consecutive numbers divisible by r!  General Math  7  
An Infinite Product  Calculus  3  
infinite product  General Math  2  
Infinite product  Calculus  2  
infinite product  Linear & Abstract Algebra  13 