Product of Terms of a Sequence

Date: 04/18/2003 at 14:13:53
From: Rosi Jimenez
Subject: Terms of a sequence

My 13-year-old son was assigned the following math problem with very 
little instruction given. Nowhere was it explained how to find the 
product of a sequence. The problem is:

Find the product of the first 99 terms of the sequence 1/2, 2/3, 3/4, 
4/5, . . .

We have found a pattern in the sequence. When 1 is added to the 
numerator and denominator of each term, the next term is produced. 
However, we are totally stumped as to how to multiply terms in a 
sequence. Please help me explain this to my son.  

Thank you.

Date: 04/18/2003 at 14:23:47
From: Doctor Roy
Subject: Re: Terms of a sequence

Hi,

Thanks for writing to Dr. Math.

To find the product of two numbers, you multiply them together. Let's 
do a few from this sequence to see if you can catch the pattern:

Product of first 2 terms:

    (1/2)(2/3) = 1/3

Product of first 3 terms:

    (1/2)(2/3)(3/4) = 1/4

Product of first 4 terms:

    (1/2)(2/3)(3/4)(4/5) = 1/5

Product of first 5 terms:

    (1/2)(2/3)(3/4)(4/5)(5/6) = 1/6

Do you notice a pattern?  The product is really just multiplying all
the terms together. This isn't a problem where you have to look for a
formula, but a problem where you are supposed to think for a little 
bit and find an easy way to calculate the solution.

Does this help?  Please feel free to write back with any questions you
may have.

- Doctor Roy, The Math Forum
  http://mathforum.org/dr.math/