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I would like to know if there is a closed form way of writing this sum please:

$$\sum_{i=1}^n\frac{a}{b-x_i}$$

Rafael Bordoni
  • 145
Esmerelda
  • 45
  • It depends on what is $x_i$. Generally, there is no closed form for $\sum^n_{i=1}\frac{1}{i}$, but you can approximate it by $\log{n}$. – Rafael Bordoni Dec 10 '14 at 18:23
  • If I was playing around with a complicated expression with unknowns $x_1,\cdots,x_n$ and obtained that, I would consider it closed form and feel satisfied. – anon Dec 10 '14 at 18:26
  • Thank you. Is there a way to rewrite or approximate this expression so that I can get the term \sum_{i=1}^n x_i somewhere in it? I also know that 0 \leq x_i \leq 1 \ \forall i. – Esmerelda Dec 11 '14 at 10:50

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