Evaluate Series: sin(pi)(sq. rt. (n^2+k^2))

  • Thread starter Thread starter A00446849
  • Start date Start date
  • Tags Tags
    Series
Click For Summary
SUMMARY

The discussion centers on evaluating the infinite series defined by the expression sigma from n=1 to infinity of sin(pi * sqrt(n^2 + k^2)). Participants confirm that the sine of pi equals zero, leading to the conclusion that the entire series evaluates to zero. The importance of correctly typing mathematical expressions is emphasized, as it directly impacts the evaluation of the series.

PREREQUISITES
  • Understanding of infinite series and convergence
  • Knowledge of trigonometric functions, specifically sine
  • Familiarity with square root operations in mathematical expressions
  • Basic algebraic manipulation skills
NEXT STEPS
  • Research the properties of sine functions and their periodicity
  • Explore convergence tests for infinite series
  • Learn about the implications of mathematical notation accuracy
  • Study the behavior of series involving square roots and trigonometric functions
USEFUL FOR

Students studying calculus, mathematicians interested in series evaluation, and educators teaching infinite series and trigonometric functions.

A00446849
Messages
1
Reaction score
0

Homework Statement



sigma n=1 to infinity
sin(pi)(sq. rt. (n^2 + k^2))


Homework Equations





The Attempt at a Solution

 
Physics news on Phys.org
Have you made any attempt at a solution? Moreover, have you typed that equation in correctly? (The sine of pi = 0, so the whole series as displayed above will be 0)!
 

Similar threads

Fourier series of this scale and shift of triangle wave
  • · Replies 1 ·
Replies
1
Views
2K
How should I show the following by using the signum function?
  • · Replies 14 ·
Replies
14
Views
2K
Compute sum (possibly using Parseval's formula)
  • · Replies 1 ·
Replies
1
Views
2K
Does this series converge uniformly?
  • · Replies 7 ·
Replies
7
Views
3K
Fourier series of translated function
  • · Replies 1 ·
Replies
1
Views
2K
On pointwise convergence of Fourier series
  • · Replies 3 ·
Replies
3
Views
2K
Calculating Laurent series of complex functions
  • · Replies 3 ·
Replies
3
Views
2K
The sum of this series of the product of 2 sine functions
  • · Replies 14 ·
Replies
14
Views
3K
Convergence of oscillatory/geometric series
  • · Replies 1 ·
Replies
1
Views
2K
Finding a periodic solution to ODE
  • · Replies 16 ·
Replies
16
Views
2K