Originally Posted by

**terrorsquid** I wasn't talking about your notation. I meant the $\displaystyle z_{n}$ terms. If they are just symbols then squaring both sides would give $\displaystyle z_{1}^2+2z_{1}z_{2}+z_{2}^2$ on both sides so then they are equal and the base case has held true? I don't know what they represent. I can see that it should be true as when $\displaystyle z_{n}$ is positive and $\displaystyle z_{n+1}$ is negative, then the LHS would be the absolute value of the difference and the RHS would still be the sum of the two absolute values and therefore the RHS would be greater. Obviously if both terms are positive then they are equal. But, again, I don't know what the terms represent in this example.