Simplfication of a sigma notation

In summary, AerospaceEng tries to solve a homework equation but is having difficulty. He is unsure how to proceed and needs help.
  • #1
AerospaceEng
28
0

Homework Statement



1/1(4) + 1/4(7) + 1/7(10)+...+ 1/(3n-2)(3n+1)

and the sigma notation is pretty obvious

Homework Equations



nothing really..

The Attempt at a Solution



I can see an obvious pattern its n(n+3) but n cannot be 2,3,5,6 etc.. and the second digit in the first term becomes the first digit in the next term. I think its fairly simply but I've just been staring at it blankly and i think I've passed that point where I am doing any useful thinking so an answer or even a hint would be great.
 
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  • #2
Hi AerospaceEng! :smile:

Are you asking how to write it with a ∑ ?

If so, the answer's in the question: it's ∑ 1/(3n-2)(3n+1) :wink:

(and btw the next step is probably to use partial fractions)
 
  • #3
no lol but thank you, i definitely know how to write it in sigma but now that i have it in a "complex" sigma form I need to change it to a more simplified sigma notation so like i tried:

∑ 1/(n)(n+3) but that doesn't work for 2,3 and so on like i mentionned before

and then after wards i have to prove that my simplification works by the principle of mathematical induction. But i can do that part its just changing the sigma
 
  • #4
oh good! :biggrin:

in that case, it is partial fractions …

ie, ∑ [ A/(3n-2) + B/(3n+1)) ] :wink:
 
  • #5
no, I don't think so. well not in my case anyways I haven't learned that.
Thanks for trying, I'll post the answer once I figure it out to clarify what i needed.
 
  • #7
Okay so I have the answer now the sum of the series is equal to n/(3n+1) that's what i needed. but thanks anyways tim I really appreciate it
 

What is sigma notation?

Sigma notation is a mathematical shorthand used to represent a series of numbers or terms. It is written as Σ with a variable below and numbers or terms above and below the sigma symbol.

Why is sigma notation used?

Sigma notation is used to simplify the representation of a series of numbers or terms in a concise and efficient way. It also allows for easy manipulation and calculation of the series.

How do you simplify a sigma notation?

To simplify a sigma notation, you can use the following steps:

  1. Identify the starting and ending values of the variable below the sigma symbol.
  2. Write out the numbers or terms above the sigma symbol, replacing the variable with each value from the starting to ending value.
  3. Add or subtract the resulting numbers or terms to get the simplified form.

Can sigma notation be used for any type of series?

Yes, sigma notation can be used for any type of series, including arithmetic, geometric, and infinite series.

Are there any rules or properties of sigma notation?

Yes, there are several rules and properties of sigma notation, including the commutative and distributive properties, as well as the rule for changing the limits of the variable. It is important to understand these rules in order to manipulate and simplify sigma notation correctly.

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