What is the result of adding a HP series to a fraction sequence?

  • Context: High School 
  • Thread starter Thread starter Puneeth423
  • Start date Start date
  • Tags Tags
    Series Sum
Click For Summary
SUMMARY

The discussion focuses on calculating the sum of a harmonic series, specifically the sequence 1/5 + 1/7 + ... + 1/401. Participants suggest using the Euler-product formula with a(n) = n^(-s-1) for theoretical insights, while also recommending computational methods for explicit results. A practical approach includes averaging the sum of the first 200 terms of the series by calculating (1/2 + 1/3 + 1/4 + ... + 1/200)/2.

PREREQUISITES
  • Understanding of harmonic series and their properties
  • Familiarity with Euler-product formulas
  • Basic programming skills for computational analysis
  • Knowledge of mathematical summation techniques
NEXT STEPS
  • Explore the Euler-product formula in depth
  • Learn how to implement series summation in Python using libraries like NumPy
  • Investigate the convergence properties of harmonic series
  • Study advanced techniques for approximating infinite series
USEFUL FOR

Mathematicians, computer scientists, and students interested in series convergence and computational mathematics.

Puneeth423
Messages
51
Reaction score
0
1/5 + 1/7 + ..... + 1/401
 
Mathematics news on Phys.org
Hey Puneeth423.

Try considering the Euler-product with a(n) = n^(-s-1) or if you want to find the result explicitly use a computer.
 
Try adding (1/2 + 1/3 + 1/4 + .. + 1/200)/2.
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
1K
  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 4 ·
Replies
4
Views
3K
Replies
8
Views
2K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K