Let me try again

Let me make a test
This is an inline math :$\sum_{i=1}^nx_iy_i\leq\sqrt{\sum_{i=1}^nx_i}\sqrt{\sum_{i=1}^n y_i}$
This is in display math: $$\sum_{i=1}^nx_iy_i\leq\sqrt{\sum_{i=1}^nx_i}\sqrt{\sum_{i=1}^n y_i}$$
New line
$$\sum_{i=1}^nx_iy_i\leq\sqrt{\sum_{i=1}^nx_i}\sqrt{\sum_{i=1}^n y_i}$$

$\begin{tabular}{c|c|c}a&b&c\\d&e&f\end{tabular}$

More sample

Math equations (non-LaTeX)in Blogger using bigger than and less than symbols: If $x \textless i$ then the value of the wave function oscillates in such a way that for m 5 for the probability distribution when $h < a$ in the limits of the boundary conditions.

Latex Samples

Here is an inline math $\sum_{i=1}^nx_iy_i$ and $\displaystyle \sum_i^n a_i$ this is a display math $$\sum_{i=1}^nx_iy_i$$ . You can hover your mouse over the math symbols to see the corresponding latex code.
$$\sum_{i=1}^n a^2+b^2$$
If you dont't like the border around the image, go to the dashboard---> layout ---> edit html and look at the following code

.post img {
border:1px solid #CCCCCC;
padding:4px;
}

and remove the second line (border:... etc) or replace 1px into 0px.

Here are more examples:

Matrix
$\begin{pmatrix}a&b&c\\d&e&f\\g&h&i\end{pmatrix}$

Multiline Equation
$\begin{aligned}x^2+4x-21&=0\\x^2+4x&=25\\x^2+4x+4&=21+4\\(x+2)^2&=25\\x+2&=\pm 5\\x&=-2\pm 5\end{aligned}$

Commutative Diagram
$\usepackage[all]{xy}\xymatrix{0\ar[r]&A\ar[d]\ar[r]^f&B\ar[d]&\\&C\ar[r]_g&D\ar[r]&0}$

With Color
$\color{Magenta}\usepackage[all]{xy}\xymatrix{0\ar[r]&A\ar[d]\ar[r]^f&B\ar[d]&\\&C\ar[r]_g&D\ar[r]&0}$

$\color{Blue}A^2+z^5$
$\begin{tabular}\tiny{a}&\scriptsize{b}\end{tabular}$