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

Here's the result:In summary, the conversation discusses finding the summation from 1 to 100 of the equation Σ (1/k) - (1/(k+1)). The user is unsure of how to approach the problem but is guided to write out the first few terms and discover a pattern. This method helps the user to solve the problem.
  • #1
Leah123rose
5
2
Member warned that some effort must be shown, not just described

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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  • #2
So write out ##{1\over k} - {1\over k-1}## to start with ...
 
  • #3
Or better: write out the first five terms and discover a pattern...
 
  • #4
Oh, and read the guidelines . This post is not up to PF standards

:wink:
 
Last edited by a moderator:
  • #5
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.
 
  • #6
Okido !
 

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

What is a summation equation?

A summation equation is a mathematical expression that represents the sum of a series of numbers or terms. It is denoted by the symbol Σ (sigma) and is often used to find the total value of a sequence or pattern.

How do you solve a summation equation?

To solve a summation equation, you can use efficient methods such as the telescoping method, the partial fraction method, or the geometric series method. These methods involve simplifying the equation, applying known formulas, and using algebraic manipulation to find the solution.

What is the telescoping method for solving summation equations?

The telescoping method involves simplifying each term in the summation equation and canceling out terms that occur in both the numerator and denominator. This results in a single term or a few terms that can then be evaluated to find the solution.

What is the partial fraction method for solving summation equations?

The partial fraction method involves breaking down the fraction in the summation equation into simpler fractions using a technique called partial fraction decomposition. This allows the summation equation to be rewritten in a form that is easier to solve.

What is the geometric series method for solving summation equations?

The geometric series method is used specifically for summation equations that involve a geometric sequence. It involves using the formula Σ(ar^n) = a / (1-r) to find the sum of the series. This method is useful when dealing with infinite summation equations.

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