sigma

[tsh44]

Hello, I am having trouble evaluating this sigma problem:

There is a sigma sign with (k=1) underneath and 20 above. To the right is
3k (k+2) .

I started plugging in numbers and got the series 9+24+45+72 but i don't see pattern. Any help would be appreciated.

 

[ChaoticLlama]

Does it help at all when it looks like this?

\(\displaystyle \L\sum\limits_{k = 1}^{20} {(3k)(k + 2)} = \sum\limits_{k = 1}^{20} {(3k^2 + 6k)} = 3\sum\limits_{k = 1}^{20} {k^2 + 6\sum\limits_{k = 1}^{20} k }\)

 

[stapel]

Is the summation as follows?

. . . . .\(\displaystyle \large{\begin{array}{c}20\\\Sigma\\k=1\end{array}\,3k(k\,+\,2)}\)

If so, I would manipulate the "3k(k + 2)" as "3k² + 6k", and then break up the summation as "3-sum-k² + 6-sum-k". There should be formulas for the k² and the k that you can apply.

Eliz.

 

[tsh44]

Um not really....is there some rule i need to know?

 

[stapel]

Did the book/class not mention any summation formulas...? :shock:

Thank you.

Eliz.

 

[ChaoticLlama]

Um not really....is there some rule i need to know?

That is disheartening to hear. If you either missed the class or neglected to take appropriate notes, I would recommend that you do the following: do research on the topic yourself. It's not hard at all to solve from the work we gave you. Post back with your results.