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HELP!!!Questions on summing series?
Can anyone find the sum of the series 1/r ,where the first term of r=1,last term of r=n .
5 Answers
- Steven CLv 41 decade agoFavorite Answer
The series doesn't have a 'nice' closed form expression, although there are some nice approximations and inequalities for the sum.
The sum you are describing is part of the harmonic series. The harmonic series itself diverges to infinity.
For the sum to n terms (written H_n):
ln (n + 1) < H_n < 1 + ln n
H_n ≈ ln n + γ
where γ is the Euler-Mascheroni constant, approximately 0.5772156649015... more information at http://mathworld.wolfram.com/Euler-MascheroniConst... or http://en.wikipedia.org/wiki/Euler%E2%80%93Mascher...
The sum to n terms does have an exact representation, although it involved special functions which are only really encountered in high level maths.
H_n = γ + ψ0(n + 1)
where ψ0 is the digamma function more information at http://mathworld.wolfram.com/DigammaFunction.html
- Anonymous1 decade ago
The answer is 1n
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