Partial sum of harmonic series as an improper fraction

AI Thread Summary
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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