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# FP1 - is there a standard formula for this?

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1. So, as basically anyone who has done FP1 knows, there are many standard formulae for the summation of n, n^2 and n^3 and so on.

Summation from n = 1 to n = k for n^2 would be n(n+1)(2n+1)/6, and so on.

But is there a standard formula for the summation of the reciprocals, i.e:

Summation from n = 1 to n = k for 1/n

Many thanks.
2. This is a harmonic progression and I do not think it is on the syllabus. I do not think there is a formula but there are approximations with logs in.
3. (Original post by Dermatome)
So, as basically anyone who has done FP1 knows, there are many standard formulae for the summation of n, n^2 and n^3 and so on.

Summation from n = 1 to n = k for n^2 would be n(n+1)(2n+1)/6, and so on.

But is there a standard formula for the summation of the reciprocals, i.e:

Summation from n = 1 to n = k for 1/n

Many thanks.
Nopes. You're dabbling dangerously close to maths we don't know much about; let alone be in a FP1 syllabus. Have a look at the Riemann Zeta function for more fun.
4. (Original post by Zacken)
Nopes. You're dabbling dangerously close to maths we don't know much about; let alone be in a FP1 syllabus. Have a look at the Riemann Zeta function for more fun.
Lol.

I know only a very small amount about Riemann's Hypothesis. It goes beyond my understanding of maths, but at least it is related to FP1 in the sense that complex numbers are involved.
5. (Original post by nerak99)
This is a harmonic progression and I do not think it is on the syllabus. I do not think there is a formula but there are approximations with logs in.
(Original post by Zacken)
Nopes. You're dabbling dangerously close to maths we don't know much about; let alone be in a FP1 syllabus. Have a look at the Riemann Zeta function for more fun.
Many thanks for both of your replies.
6. (Original post by Dermatome)
Many thanks for both of your replies.
There is a lot of nice things that can be done with harmonic progression without even dreaming of any zeta functions although if you want to sound good then the Riemann anything is a good place to go.

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