safak

Well, it is no homework. I stumbled upon this in the book 'Concrete Mathematics' from Graham,Knuth,Patashnik page 439 about Asymptotics and I don't get it, so I considered asking someone. It just says 'here is a series which has no closed form but which can be approximated to (1) and (2).", (1) and (2) refering to the above answers. I totaly don't know how to calculate series. This is a science forum - why do you even bother about someone asking a question she/he apperently can't solve themselves. Some people learn more if their questions are answered, their grades are given by their teachers, and it is no use banging my head against this series if I don't know how to solve, i will look no good in ten years except some divinity beams the answer into my head Since my main to be learned chapter is not solving series but Asymptotics.

Hi all! how can I approximate the series: [math] S_{n} = \sum_{k=0}^{n}\binom{3n}{k} [/math] ? The approximation is necessary, since no closed form can be found. Solutions are: [math] S_{n} \sim 2\binom{3n}{n} [/math] or more precise [math] S_{n} = \binom{3n}{n}(2-\frac{4}{n}+\mathcal{O}(\frac{1}{n^2})) [/math] but how did I get there? Thanks! safak