$x + y$



\

python
x=12

test

```python

for i in range(3): print(str(i))

```

```python x = 12 for i in range(3): print(i)

```

**The Cauchy-Schwarz Inequality**

$$\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)$$

The Cauchy-Schwarz Inequality

$\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)$

for i in range(3):
    print(str(i))

def index
  puts "hello world"
end