speed converge to v1+v2It can be proved (you can check my answers in "第二题：条件足够了"). Ok, I get your meaning. You are trying to discretize the problem using time slice of 1 sec, right? You can use this kind of method, although it makes problem unnecessary complex (remember not to fix the time slice, you should calculate the limit when time slice approach 0). I use this approach as well, of course, for computer programming, and the time slice is usually set to sufficiently small value to get accuracy answer. The cause of the problem is that you set the time slice to 1 sec. During this 1 sec period, the worm moves some not negligible distance already. Using time slice of 1, the worm speed: .01 * ( 1 + 1/n + 1/n*(n-1) + 1/ n*(n-1)*(n-2) ... ) < .01 * ( 1 + 1/n + 1/n + ... ) = .02 I.e. the method itself poses a problematic constraint on the problem. Try set the time slice smaller.