my bad I wasn't specific enough. I meant the partial sum.martinbn said:Do you mean the sum? It is divergent! Or do you mean the partial sums? Or something else?
What is that for the harmonic series?al4n said:my bad I wasn't specific enough. I meant the partial sum.
what do you mean?martinbn said:What is that for the harmonic series?
Well, you said.al4n said:what do you mean?
It sounds like you can figure out the case of the harmonic series, and want to do the same with the more general. Is it not what you mean?al4n said:it "looks" like a harmonic series but not in the form I'm capable of figuring out.
help.
I guess. Is that not already figured out? Looking around, What I thought was the formula was in fact only an approximation. So what I should've first asked is, is there something like that to the specific examplemartinbn said:Well, you said.
It sounds like you can figure out the case of the harmonic series, and want to do the same with the more general. Is it not what you mean?
So to be clear: you are looking for a formula for ##f(m;c,k)=\displaystyle{\sum_{n=1}^m}\dfrac{1}{c+kn}## for any parameters ##c,k \in \mathbb{R}##?al4n said:I guess. Is that not already figured out? Looking around, What I thought was the formula was in fact only an approximation. So what I should've first asked is, is there something like that to the specific example
A harmonic(ish) series is a mathematical series that closely resembles a harmonic series, which is the sum of the reciprocals of the natural numbers. In a harmonic(ish) series, the terms may deviate slightly from the exact reciprocals of the natural numbers, but still exhibit similar properties.
Finding a general formula for a harmonic(ish) series can help in understanding the behavior and properties of such series, and can be useful in various mathematical applications and calculations.
The general formula for a harmonic series is given by: 1 + 1/2 + 1/3 + 1/4 + ... + 1/n = ln(n) + γ, where ln(n) is the natural logarithm of n and γ is the Euler-Mascheroni constant.
Deriving a general formula for a harmonic(ish) series involves analyzing the pattern of the series and determining a formula that can express the sum of the terms in the series. This may require knowledge of calculus, algebra, and series analysis.
Harmonic(ish) series can exhibit interesting properties such as convergence or divergence, and can be used in various mathematical and scientific contexts such as in physics, engineering, and finance for modeling and analysis purposes.