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actually, I need to calculate an infinite sum of fractions. The problem is that the Limit of the sum is part of the summands. The formula looks like this:

[tex]\lim_{n \to \infty} \sum_{i=1}^{n} \frac{1}{n(1 + \lambda + \sigma^2)-i(1+\lambda)}[/tex],

where 'itex]\sigma[/itex] and [itex]\lambda[/itex] are constants. Numerically, this infinite sum converges to a value that can be interpreted as a first order approximation of a channel capacity for some communication scheme.

My idea to determine this limit is to calculate the finite sum of n terms first. Since, in this case, n is constant, the sum can be written as:

[itex]\sum_{i=1}^{n}{\frac{1}{a-ib}}[/itex], where a > n b

When it would be possible to find a conversion of this sum, I thought it might also be possible to determine the limit for n to [itex]\infty[/itex].

If anyone has ideas how to solve the problem, I would be grateful for comments and feedback.

Thanks a lot,

Michael

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# Infinite Sum of Fractions

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