Partial sum of harmonic series as an improper fraction

[starfish99]

I am interested in calculating a a partial sum of harmonic series as an improper fraction.

I added 1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10 with my calculator by finding a common denominator and got the fraction 6 999 840/3 628 800. It would take some time to do it for 1/2+1/3+...1/100.

Is there any program that can create these fractions for any partial harmonic sum?

 

[ArcanaNoir]

Your calculator didn't simplify. $\frac{6999840}{3628800}$ simplifies to $\frac{4861}{2520}$ .

As for doing it up to 100, does your calculator do sums? I have a casio classpad, which is similar in capabilities to a TI 89, and it does sums.

Woah, I just had it do up to 1/100, and it's loooooooong. If your calculator isn't going to simplify it, it's going to be crazy.

From what I hear a TI 83 will do it.

 

[Gib Z]

http://www.wolframalpha.com/input/?i=sum+k=1+to+k=100+1/k

 

[starfish99]

Thanks Gib Z

 

[CellCoree]

I find your interest in calculating the partial sum of harmonic series as an improper fraction to be intriguing. This series, also known as the harmonic sequence, is a fundamental concept in mathematics and has been studied extensively. While it may seem daunting to calculate these fractions by hand, there are indeed programs and mathematical tools that can assist in this process.

One approach is to use a computer program such as Mathematica or Matlab, which have built-in functions for calculating partial sums of harmonic series and representing them as fractions. These programs also have the ability to generate fractions for any partial harmonic sum, making it easier to explore and analyze different cases.

Another option is to use a mathematical formula, such as the one given by Leonhard Euler, which allows for the calculation of the nth partial sum of the harmonic series. This formula can be used to generate fractions for any desired partial sum.

Additionally, there are online resources and calculators available that can also assist in calculating and representing partial sums of harmonic series as fractions.

In conclusion, while it may take some time to manually calculate these fractions, there are various tools and methods available for generating them for any partial harmonic sum. I encourage you to continue your exploration of this fascinating concept and utilize these resources in your calculations.