Partial sum of harmonic series as an improper fraction

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Calculating the partial sum of the harmonic series as an improper fraction can be complex, as demonstrated by the example of summing 1/2 to 1/10, which results in the fraction 6,999,840/3,628,800 that simplifies to 4861/2520. Users are seeking programs or calculators that can handle these calculations and simplify the results automatically. The discussion mentions that advanced calculators like the Casio ClassPad and TI-89 can perform these sums, while the TI-83 is also noted for its capabilities. For larger sums, such as up to 1/100, the output can be lengthy and cumbersome if not simplified. Online tools like Wolfram Alpha are suggested for handling such calculations efficiently.
starfish99
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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?
 
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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.
 
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Thanks Gib Z
 

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