Questions for first year students at the University. I will help teach in a introductory class in mathematics for engineers in applied math at the University.
Anyone have any good and cool favorite questions or know where I can find some?
Anything is welcome
For the moment there is some questions like


*

*write: $1 + 2 + 3 + ... + 100$ as a sum

*show that $XY-YX = I$ has no solution for square matrices.

*$p | (n^2 - n)$ ($p$ is prime).


Thanks

Try asking students to solve for $x$ in the equation $x+\sin(x)=0$. 
The solution $x=0$ seems trivial, but it can only be solved by numerical methods, a course of which engineering majors will benefit greatly from.
