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Algebra/Series to sigma notation

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Question
Hi Abe,

I have a question where there is a series that goes like this: (3/5)+(4/6)+(5/7)+(6/8)+(7/9) and I've been able to change it into a sigma notation where n=7 and k=3 and the equation= (k/k+2). But I just don't quite know how to properly show my work for this problem algebraically?

Many Thanks,
Sam

Answer
Hello Sam,

What work do you mean?  Just to show that k/(k+2) gives the kth term?

If you *must* show work, I would just show:
3/5 = 3/(3+2)
4/6 = 4/(4+2)
5/7 = 5/(5+2)
...
which suggests the following pattern: k/(k+2), where k=3, 4, 5, 6, 7

Abe

Algebra

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Abe Mantell

Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Experience

Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

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