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# Algebra/Series to sigma notation

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

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

Volunteer

#### 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