Efficient Methods for Solving Summation Equations: Σ(1/k) - (1/(k+1))

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    Calc 2 Summation
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SUMMARY

The forum discussion focuses on solving the summation equation Σ(1/k) - (1/(k+1)) for k ranging from 1 to 100. Participants suggest writing out the first five terms to identify a pattern, which aids in understanding the solution. The discussion emphasizes the importance of adhering to forum guidelines for quality contributions. Overall, the exchange highlights effective strategies for tackling summation problems in mathematics.

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  • Understanding of basic summation notation and properties
  • Familiarity with the concept of series and sequences
  • Knowledge of mathematical patterns and their identification
  • Basic algebraic manipulation skills
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  • Explore advanced techniques for solving summation equations
  • Learn about mathematical induction for proving summation identities
  • Study the properties of harmonic series and their applications
  • Investigate software tools for symbolic computation, such as Wolfram Alpha
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Students studying mathematics, educators teaching summation concepts, and anyone interested in enhancing their problem-solving skills in series and sequences.

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Homework Statement


(summation from 1 to 100) Σ (1/k) - (1/(k+1)) [/B]

Homework Equations


Σc = cn
Σi = (n(n+1))/2[/B]

The Attempt at a Solution


I can only find summation equations for variables in the numerator. I'm not sure how to even start this problem. [/B]
 
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So write out ##{1\over k} - {1\over k-1}## to start with ...
 
Or better: write out the first five terms and discover a pattern...
 
Oh, and read the guidelines . This post is not up to PF standards

:wink:
 
Last edited by a moderator:
BvU said:
Or better: write out the first five terms and discover a pattern...
That helped, thanks! Sorry my post is not up to standards, I'm a new member but will do better next time.
 
Okido !
 

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