Sum of Fractions: Solving \sum_{k=1}^{100} (\frac{1}{k} - \frac{1}{k+1})

Thread starter IniquiTrance
Start date Dec 14, 2009
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Sum

In summary, the purpose of finding the following sum is to determine the total value when a set of numbers are added together. The formula for finding the sum is <em>sum = a + b + c + ...</em>, and this differs from finding the average by involving only adding numbers together. Real-world applications for finding the sum include finance, statistics, and engineering, where it can help determine total costs, population or sample size, and total forces. Efficient strategies for finding the sum include grouping similar numbers together, using mental math techniques, and utilizing tools like calculators or spreadsheets.

Dec 14, 2009

IniquiTrance

Homework Statement

[tex]\sum_{k=1}^{100} (\frac{1}{k} - \frac{1}{k+1})[/tex]

Homework Equations

The Attempt at a Solution

Unsure how to approach this...

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Dec 14, 2009

rock.freak667

Homework Helper

consider the same series

[tex]\sum_{k=1}^{n} (\frac{1}{k} - \frac{1}{k+1})[/tex]

Now write out a few terms (k=1,k=2,k=3,k=n-2,k=n-1,k=n) and see what happens.

What is the purpose of finding the following sum?

The purpose of finding the following sum is to determine the total value when a set of numbers are added together.

What is the formula for finding the following sum?

The formula for finding the following sum is sum = a + b + c + ..., where a, b, c represent the numbers in the set.

What is the difference between finding the following sum and finding the average?

Finding the following sum involves adding a set of numbers together to determine their total value, while finding the average involves dividing the sum by the number of numbers in the set to determine the average value.

What are some real-world applications of finding the following sum?

Finding the following sum is useful in many fields, such as finance, statistics, and engineering. For example, in finance, finding the sum of expenses can help determine the total cost of a project. In statistics, finding the sum of data points can help determine the total population or sample size. In engineering, finding the sum of forces can help determine the total force acting on a structure.

What are some strategies for finding the following sum efficiently?

One strategy for finding the following sum efficiently is to group numbers that have similar values together and then add them. Another strategy is to use mental math techniques, such as rounding or breaking numbers down into smaller, easier to add numbers. Additionally, using a calculator or a spreadsheet can also help with efficiently finding the following sum.