Product of Terms of a SequenceDate: 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/ |
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