Let A be a matrix =
[1 1 1
0 1 1
0 0 1]
Find a formula for A^n(n is an element of N) and prove the formula by induction.
1) Calculate a few powers of A and try to spot a pattern.
2) Use your findings to speculate what the nth power would be.
3) Show that your formula works when n = 1.
4) Show that if your formula holds for n=k, then it also holds for n=k+1.
5) Smile, because your speculation was correct and you have just proved it by induction.
Let us know which step you get stuck on.