Stuck on Sigma Notation Problem

[Jaysun]

I've been putting off this homework until the end of spring break, and now I totally forgot how to do it. If anyone here knows how to do this problem, it'd be immensely appreciated if you could show me the steps to solve it. Thank you.

 

 

 

[Giordano]

I don't see a graph. Therefore, there is no area. The answer is zero.

[killerbeer0]

I don't see a graph. Therefore, there is no area. The answer is zero.

 

 

 

The graph isn't illustrated. It specifies an equation to be graphed and used, just doesn't graph it for you.

[Jaysun]

Well, there isn't a picture of the graph, but x^2 + 2 would be an upwards pointing parabola with an x-intercept at y = 2.

 

 

 

Edit: killerbeer0 beat me to it. Thanks. :P

[fastortoise]

In order to make room for genetics and biology, I had to push Calculus into the dark corner of my brain. Honestly, I have no idea how to do #1 or what a limit process is, but I can easily do #2 for you (the answer should be 12) by doing the quick i-already-passed-cal2-method. Sorry for the useless post.

[andylax38]

Part1: Well it's been a while since I've done a problem like this but I believe the answer is zero. Your taking the limit as n is approaching infinity and since in the problem n is in the denominator of 2/n as n goes to infinity 2/n gets very small and can be said that it goes to zero. If you assume that part of the problem goes to zero the then zero times any number = 0 so the whole thing = 0. Anyway I think thats right but you might want to check with someone else.

 

 

 

 

 

Part2: It's just a simple integral, take the integral of x^2 + 2 from x=1 to x=3 which is x^3/3 + 2x from x=1 to x=3.

 

Then you have (3^3/3 + 2(3)) - (1/3 + 2) = 15 - 7/3 = 12 and 2/3.

 

 

 

Hope that helps.

[i_love_burritos]

What's your limitation on #1, for when n is mod 1 ?

 

 

 

Of course your asymptote will be on 1 and -1 on both axis so n =/= 0.

 

 

 

Can you make the diagram slightly neater ?

[Deiophobus]

Why do you have to use sigma notation? It would be easier if you used an integral.

 

Take the integral of x^2+2, with your upper and lower limits at 1 and 3, respectively.

 

The integral of that is (x^3)/3+2x, and using F(B)-F(a), you would get 38/3.

 

 

 

I forget how to do sigma notation though, so maybe this isn't any help.

 

 

 

edit: I should read the thread better, I didn't realize someone already posted this method.

[Utopianflame]

Well I will show you how to do the first one, its simple enough although I wont do any of the required convergence tests as judging by the level you appear to be at you wont have been taught them and thus wont be expected to use them.

 

 

 

 

 

 

I'm not going to coment on the second one as I will almost certainly vastly over complicate what you are being asked to do (as i'm not quite certain which limit process your

[Flyingjj]

Well I will show you how to do the first one, its simple enough although I wont do any of the required convergence tests as judging by the level you appear to be at you wont have been taught them and thus wont be expected to use them.

 

 

 

image

 

 

 

I'm not going to coment on the second one as I will almost certainly vastly over complicate what you are being asked to do (as i'm not quite certain which limit process your teacher expects you to use.)

 

 

 

I think there is an error in your math. When you move the 4/2n^2 to the outside of the sigma notation, you dropped the 2 in the denominator, using 4/n^2 rather than 2/n^2 .

[Utopianflame]

Well I will show you how to do the first one, its simple enough although I wont do any of the required convergence tests as judging by the level you appear to be at you wont have been taught them and thus wont be expected to use them.

 

 

 

image

 

 

 

I'm not going to coment on the second one as I will almost certainly vastly over complicate what you are being asked to do (as i'm not quite certain which limit process your teacher expects you to use.)

 

 

 

I think there is an error in your math. When you move the 4/2n^2 to the outside of the sigma notation, you dropped the 2 in the denominator, using 4/n^2 rather than 2/n^2 .

 

 

 

 

 

Well spotted but just a typo, there shouldnt be a two in the denominator in the first place, I will fix it in a moment.

 

 

 

And fixed one typo that got copy-pasted.

[Jaysun]

Darn, I should have asked for help sooner. I had to turn my assignment in this morning, so I missed the last few couple posts.

 

 

 

Thanks to everyone for their assistance in this thread. We haven't gone over the assignment due to having a substitute teacher today, but I really liked Utopianflame's clearly explained problem solving. I'll use it as a guideline for the future.

[dongleberry]

Well I will show you how to do the first one, its simple enough although I wont do any of the required convergence tests as judging by the level you appear to be at you wont have been taught them and thus wont be expected to use them.

 

 

 

I'm not going to coment on the second one as I will almost certainly vastly over complicate what you are being asked to do (as i'm not quite certain which limit process your

 

 

 

It appears they just what another sum notation where i=1 and n goes to 3 for the equation given. I don't remember exactly how it'd be worked out, and I'd just integrate it for a more accurate result.