I am very confused with complete induction. Because in every task there is something different to do, and I never know what to insert (thats my biggest problem). 
Here's the example:
Proof with complete induction. Please please help me, because I have exams coming up (I am just becoming a primary school teacher..)


  For $n\in\mathbb{N}$:
  
  $$\sum^n_{i=1}\frac{1}{(2i-1)(2i+1)}=\frac{n}{2n+1}$$



Question: drive 3 phase induction motor with only DC (not pwm) thru each phase
Answer: If you're switching the DC through 3 half-bridges, this will work just fine. Torque will be uneven at low speeds and waveforms rather nasty, but it'll work.

Beware that turning current OFF fast to an inductive load (i.e. motor) is a good way to generate very high voltages so pay attention to protective diodes. NOT 1N4001s (FAR too slow) but high speed switching, high current diodes from each motor terminal to both supply rails, and overvoltage protection on the rails...

[edit...]
The problem with PWM is not the PWM frequency, but the number of times you have to change it per revolution... 

As you are controlling it with software, there is nothing to stop you using PWM at low speed, and switching to direct (square wave) drive at high speed.