求证一道数学等式

急求证明过程：

题目背景和来源如下：（只要证明出上式，这道概率题就完全证明出来，当然这道概率题本身有很多其它更简洁的证明方法）

楼主的课程好强大啊！能透露一下学校和教材么？

题目有问题吧，t=0的时候如何做分母!

zxun 发表于 2011-12-8 20:06
楼主的课程好强大啊！能透露一下学校和教材么？

这是Brigham Young University的Probability1. 用的教材是Geoffrey Grimmett的《Probability and Random Processes》，论坛上可以找到。

1987625sun 发表于 2011-12-8 21:03
题目有问题吧，t=0的时候如何做分母!

没有问题啊，当t=0时，上式等于(k/k)*(k,0)*[(1/2)^k]=(1/2)^k

数学归纳法试试

beyondcj 发表于 2011-12-9 10:34
数学归纳法试试

这种没办法归纳吧

the solution you posted seems not right to me.. the answer should not be equal to the sum of f_n(k).. Instead maybe you should prove that the limit of f_n(k) is zero when n goes to infinity.. something like when you proved that Pr{stoppng time=infinity}=0 (here f_n(k) is actually a stopping time), then it's equivalent to Pr{S_n=k for some finite n}=1..
To prove f_n(k)->0 when n->infinity, you could just use the Stirling's formula for those factorials..