Recent content by livcon

I realized that this problem is quite easy and requires only two states, s_{0} and s_{1}, using the first one as initial state. When the machine receives either 0 or 1 in the initial state, the output function simply returns the same bit as the input as it changes state from s_{0} to s_{1}. From...

Homework Statement Construct a finite-state machine that changes every other bit, starting with the second bit, of an input string, and leaves the other bits unchanged. Homework Equations - The Attempt at a Solution Say I have the string 1001101, then I am supposed to make a...

I guess it's because in the warmup exercise I could easily add and subtract the fractions because it was all constants, but in the one involving the variable n I got stuck. So I would probably have an epiphany if someone would just write it out. This is just a matter of me not seeing the obvious...

I appreciate the help, but I'm afraid I'm still blind here, proving the equivalence in the warmup exercise is easy Hurkyl, but I just don't see it in my problem.

That's right, but in this case I've actually been staring at the problem for a while, so I'm really interested in how to do the algebra in (2). Thanks

Homework Statement Prove by induction the following summation formula: \frac{1}{1\1*2} + \frac{1}{2*3} + ... + \frac{1}{n(n+1)} = 1 - \frac{1}{n+1} n \geq 1 Homework Equations - The Attempt at a Solution Inductive step: 1. \frac{1}{1*2} + \frac{1}{2*3} + ... + \frac{1}{n(n+1)} +...