Question

Need help with integral. Have to find the upper bound of (n)Sigma(i=1): 1/(i^2) Any advice?

Answer 1

\[\sum\limits_{i=1}^n\frac1{i^2}\] ?

Answer 2

Yes, that's what it looks like. How do you go about answering it?

Answer 3

actually im not really very confident with the definition of upper bound for this question does it mean the upper bound of the sum of the terms in the sum /?

Answer 4

@abb0t

Answer 5

@zepdrix

Answer 6

upper bound of the sum, I believe. We're just supposed to prove it has an upper bound, that's the exact wording.

Answer 7

I assume that you are using the definition of the definite integral to evaluate this, correct?
By this, I mean using limits and reimann sum. Here are some formulas that will help you evaluate the integral:

In case you forgot, you will be taking the limit as n->∞
Here are the forms that i think were taught in algebra class?
\[\sum_{i=1}^{n}c = cn\]\[\sum_{i=1}^{n} i =\frac{ n(n+1) }{ 2 }\] \[\sum_{i=1}^{n} i^2= \frac{ n(n+1)(2n+1) }{ 6 }\] and \[\sum_{i=1}^{n}i^3 = \left[ \frac{ n(n+1) }{ 2 } \right]^2\]

Answer 8

I think you can see in your book for a more formal definition of the defiite integral, evaluated on some interval, usually they give you [a, b].

The number "a" is at the bottom of the integral sign and is the lower limit of the integral. and the top number "b" at the top of the integral sign is called the upper limit of the integral. I don't think they are asking you to find the upper and lower limits (you may be asked that in Calculus 2 course or Calculus BC), but not at this point.

However, in a Calculus 1 course, they do ask to find the left-hand sum and or right hand sum. If that sounds familiar.

Answer 9

this is a computer science course XD well up to the level of Calculus 2. I just forgot how to do this sort of thing because it's been at least 2 years since I finished Calculus 2.

Answer 10

Hmm, well, to find your limits of integration, that only way that I remember was to set two functions equal to each other and that was in volumes of revolution. And this doesnt look like a volume of revolutions problem first of all.
So I think you should just be using limits to evaluate and find your answer.

Answer 11

so how do you go about using the limits to evaluate?

Answer 12

use the formulas I provided earlier to sub for i and take the lim n->∞