Finding the Limit of a Summation with Infinite Terms

  • Thread starter Thread starter cleopatra
  • Start date Start date
  • Tags Tags
    Sum
Click For Summary
SUMMARY

The discussion focuses on finding the limit of the summation of the series defined by the formula ∞ lim (sum)(1/n^2) as n approaches infinity. Participants clarify that the limit of 1/n^2 as n approaches infinity is indeed 0, but the summation of the series converges to a specific value. The final solution to the summation is known to be π²/6, a well-established result in mathematical analysis.

PREREQUISITES
  • Understanding of limits in calculus
  • Familiarity with infinite series and convergence
  • Knowledge of the Basel problem and its solution
  • Basic proficiency in mathematical notation and summation
NEXT STEPS
  • Study the Basel problem and its historical significance
  • Learn about convergence tests for infinite series
  • Explore the Riemann zeta function and its applications
  • Investigate advanced topics in series summation techniques
USEFUL FOR

Students in calculus, mathematicians interested in series convergence, and educators teaching mathematical analysis concepts.

cleopatra
Messages
45
Reaction score
0

Homework Statement


∞
lim "sum"(1/n^2)
n→∞ n=0

Can you help me find the final solution?


The Attempt at a Solution



lim (1/n^2) = 0 ?
n-∞

But the "sum" confuses
 
Physics news on Phys.org
Lim_{n \rightarrow \infty} \Sigma \left( \frac{1}{n^{2}}\right) So sum each successive term \frac{1}{1}+\frac{1}{2^{2}}+\frac{1}{3^{2}}+\frac{1}{4^{2}}+\frac{1}{5^{2}}...
 
Last edited:
There must be a way to find a final solution (with only one number).
Anybody?
 

Similar threads

How to show that these sequences are summable?
  • · Replies 1 ·
Replies
1
Views
2K
Prove that this series converges uniformly on R
  • · Replies 4 ·
Replies
4
Views
2K
Interval of convergence of power series from ratio test
  • · Replies 2 ·
Replies
2
Views
2K
Real analysis: prove the limit exists
  • · Replies 13 ·
Replies
13
Views
4K
If a series converges with decreasing terms, then na_n -> 0
  • · Replies 3 ·
Replies
3
Views
3K
Find the limit of the sum of the areas of all these triangles
  • · Replies 7 ·
Replies
7
Views
2K
Problem 1-23 and 1-24 from Spivak's Calculus on Manifolds
  • · Replies 6 ·
Replies
6
Views
2K
Show that the limit (1+z/n)^n=e^z holds
  • · Replies 6 ·
Replies
6
Views
3K
On the ratio test for power series
  • · Replies 2 ·
Replies
2
Views
2K
Computing a limit involving a square root: what is wrong?
  • · Replies 14 ·
Replies
14
Views
2K