- #1
flyerpower
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Homework Statement
[itex]\sum_{1}^{inf}[/itex] k^2/(n^3+k^2)
The Attempt at a Solution
I think it's Riemann but i cannot find a suitable function to integrate.
flyerpower said:Homework Statement
[itex]\sum_{1}^{inf}[/itex] k^2/(n^3+k^2)
The Attempt at a Solution
I think it's Riemann but i cannot find a suitable function to integrate.
Gib Z said:Please take more care to expressing to others (and yourself) what it is you want to find. As written the sum doesn't make total sense. It could be what Susanne217 said above, or Riemann sum comment makes me think you could have also meant [itex]\displaystyle\lim_{n\to\infty} \sum_{k=1}^n \frac{k^2}{n^3 + k^2} [/itex].
Gib Z said:In the case that it is what I thought, then it's not as simple as recognizing it as a pre-prepared Riemann sum. With some careful estimates to bound the sum, you should get the result to be [itex]1/3[/itex].
flyerpower said:First of all sorry for misspelling.
I used the bounds k^2/(n^3+n^2) <= k^2/(n^3+k^2) <= k^2/(n^3+1) and i worked it out to 1/3.
An infinite series is a sum of infinitely many terms. Each term is added to the previous one, creating a potentially infinite sequence of numbers.
A Riemann sum is a finite approximation of an infinite series. It uses a specific number of terms to estimate the value of the infinite series.
The Riemann zeta function is a mathematical function that represents the sum of the reciprocals of all positive integers raised to a given power.
The Riemann hypothesis is a conjecture in mathematics that suggests a connection between the distribution of prime numbers and the behavior of infinite series, specifically the Riemann zeta function.
Infinite series have many applications in physics, engineering, and other fields. They can be used to model natural phenomena, solve differential equations, and optimize systems.