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

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    Calc 2 Summation
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The discussion focuses on solving the summation equation Σ(1/k) - (1/(k+1)) from 1 to 100. Participants suggest starting by writing out the first five terms to identify a pattern, which proved helpful for the original poster. The importance of adhering to forum guidelines is also mentioned, emphasizing the need for clearer posts. Overall, the conversation highlights strategies for tackling summation problems and encourages new members to improve their contributions. Engaging with the community can enhance understanding of complex mathematical concepts.
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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 !
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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