1. $\displaystyle 1 + \cfrac{1}{2 + \cfrac{1}{3 + \cfrac{1}{4 + \cfrac{1}{5+\ddots}}}}$

2. $\displaystyle \begin{array}{|c|c|c|c|c|}\hline\mathbf{i}&\mathbf {x_i}&\mathbf{y_i}&\mathbf{x_iy_i}&\mathbf{x_i^2}\ \\hline1&0.62&2,\!8&1.736&0.3844\\\hline2&0.64&2.7 &1.728&0.4096\\\hline3&0.66&2,\!6&1.716&0.4356\\\h line4&0.68&2.5&1.7&0.4624\\\hline5&0.70&2.5&1.75&0 .49\\\hline\mathbf{\Sigma}&3.3&13.1&8.63&2.182\\\h line\end{array}$

Yes!

3. ## test

$\displaystyle \int (x-1) e^\frac{-x}{2}$

$\displaystyle -2(x-1) e^\frac{-x}{2} - 4 e^\frac{-x}{2}$

$\displaystyle \int x e^\frac{-x}{2} - \int e^\frac{-x}{2}$

4. $\displaystyle E = m c^2$

5. We no longer seem to need a matching "\right".

E.g.
$\displaystyle \left(\dfrac12$
which isn't very useful.

But also
$\displaystyle \left\{\begin{array} {l l}a_1x_1+a_2x_2+a_3=0 & \quad\text{(1)}\\ b_1x_1+b_2x_2+b_3=0 & \quad\text{(2)} \end{array}$
...which is!

(Previously it was necessary to match the "\left\{" with a corresponding "\right." to avoid a syntax error. At least, I think it was ...)

Hmm... Interesting.