- #1
Justabeginner
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- 1
Homework Statement
Find Ʃ(product) with k=1 as the lower limit, and 50 as the upper limit. The formula is k/(k+2)
Homework Equations
The Attempt at a Solution
I noticed a pattern where the first few numbers are:
1/3, 2/4, 3/5, 4/6, 5/7 The denominator should cancel with the numerator of the next number in the pattern. I noticed this pattern for the odd numbered fractions. The last number in this odd numbered series will be 49/51, for which there are no cancellations possible, I think. For the even numbers, the pattern starts with 2/4 and ends with 50/52.
I think the fraction left will be (1*2)/(51*52)= 1/(51*26)
Is this logic right? I at first thought ..there is NO way they want me to multiply it out, and then realized there must be a pattern. So I tried and I hope I've got something. Thanks!