How to evaluate sigma notation

Hi everyone! I am completely new to Matlab and am in need of great help.

I have to find the algebraic sum of (n sigma i=1) (5/n) ((5i/n)^4 + 5(5i/n)^2 + 5i/n)

I am totally lost. Thank you so much if you can help!

[Jan]

The shown notation is not clear. Which are the limits of the sum?

Answer 1

[Jan]

For homework questions the usual proceding is, that you show, what you have done so far and ask a specific question. Then you have the chance to submit the solution without cheating.

Answer 2

[Yuna Kim]

Well, ultimately the question is asking to take the sum to infinity so n isn't defined but the initial question is to express the area under the curve y=x^4 + 5x^2 + x from 2 to 7 as a limit.

I'm asking for part b which asks to use a computer algebra system (matlab) to evaluate the sum in part (a).

Btw, thanks for asking!

Answer 3

[Walter Roberson]

syms i n
symsum(5*((5*i/n)^4..., i, 1, n)

However, this does not appear to have anything to do with that integral.

[Yuna Kim]

We have to ultimately take the limit to infinity to find the actual sum. I did everything by hand already but have to show it through matlab as well, which is what I am having trouble with. I should be able to find the area if I take the limit to infinity.

I have entered limit (3125/n^4 - 625/n^2 + (25*sqrt(-1))/n, n, infinity) but it is giving me zero which makes me think that I got the summation wrong.

Am I doing something wrong?

[Yuna Kim]

also i^2 should equal n(n+1)(2n+1)/6 and so on.