## Fill-in-the-blank Induction Exercises

1. Use mathematical induction to show that 3 + 4 + ... + n-2 = (n+1)(n-4)/2, n>=5.
```Base case: n=____.  Left side:________________  Right side:__________________

Inductive step:

If _____________________________________  then ____________________________________.
(property for k)                         (property for k+1)

=> ____________________________________
(simplify property for k+1)

Proof:
By the inductive hypothesis, ________________________________________________.

To make the left side of this look like what we are trying to show, add

___________ to both sides.

This gives ___________________________________________________________________.

Simplifying, we get __________________________________________________________

______________________________________________________________________________.
```

2. Use mathematical induction to show that 1 + 2 + ... + n+1 = (n+1)(n+2)/2
```Base case:

Inductive step:

Proof:
By the inductive hypothesis, _________________________________________________.

(... You finish!)

```