Methods of Proof
Exhaustion
Sum of consecutive square numbers between 100 and 200
100, 121, 144, 169, 196
- 100+121 = odd
- 121+144 = odd
- 144+169 = odd
- 169+196 = odd
Counter Example
Sum of two consecutive prime numbers is always even
2+3=5 is odd
\(\therefore\) this is not true.
\(\frac{x}{y} + \frac{y}{x} \ge 2\)
