Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am struggling to find an answer of the following series

$$\sum_{i=1}^n \frac{1}{1+\exp(a_i+b_ix)}$$

Any suggestion?

share|improve this question
Any information what $a_i$ and $b_i$ are? –  Fabian Oct 5 '12 at 15:20
This is no series as it has only $n$ terms... What exactly do you want to calculate? –  Sh4pe Oct 5 '12 at 15:25
I'm confused by the question. What makes you think this series converges? What's the motivation here? It will help to know that. –  000 Oct 5 '12 at 15:27
$a_i$ and $b_i$ are any number in R. I need to find an equal expression which includes $e^{\sum _i^n a_i}$ and $ e^{\sum _i^n b_i}$ –  user43754 Oct 5 '12 at 22:38
I don't think you will find an expression in terms of $\exp(\sum a_i)$ and $\exp(\sum b_i)$ Note that if one $a_i$ is very large, the corresponding entry into the sum is essentially zero and doesn't matter. When you add all the $a_i$ it will dominate. –  Ross Millikan Oct 5 '12 at 22:48

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.