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