Question

some other example
$\frac{7}{2} y = \frac{2}{7}$
​

Answer 1

Answer:

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Answer 2

Answer:

this is an example of this question

it is very big example

Step-by-step explanation:

Subscripts and Superscripts

Subscripts and superscripts (such as exponents) can be made using the underscore _ and carat ^ symbols respectively.

Symbol Command Symbol Command

$2^{2}$ 2^2 $\textstyle a_i$ a_i

$\textstyle 2^{23}$ 2^{23} $\textstyle n_{i-1}$ n_{i-1}

$a^{i+1}_3$ a^{i+1}_3 $x^{3^2}$ x^{3^2}

$2^{a_i}$ 2^{a_i} $2^a_i$ 2^a_i

Notice that we can apply both a subscript and a superscript at the same time. For subscripts or superscripts with more than one character, you must surround with curly braces. For example, x^10 produces $x^10$, while x^{10} produces $x^{10}$.

Math Commands

Here are some commonly used math commands in LaTeX:

Fractions

Symbol Command

$\frac {1}{2}$ \frac{1}{2} or \frac12

$\frac{2}{x+2}$ \frac{2}{x+2}

$\frac{1+\frac{1}{x}}{3x + 2}$ \frac{1+\frac{1}{x}}{3x + 2}

Notice that with fractions with a 1-digit numerator and a 1-digit denominator, we can simply group the numerator and the denominator together as one number. However, for fractions with either a numerator or a denominator that requires more than one character (or if the numerator starts with a letter), you need to surround everything in curly brackets.

Use \cfrac for continued fractions.

Expression Command

$\cfrac{2}{1+\cfrac{2}{1+\cfrac{2}{1+\cfrac{2}{1}}}}$ \cfrac{2}{1+\cfrac{2}{1+\cfrac{2}{1+\cfrac{2}{1}}}}

Radicals

Symbol Command

$\sqrt{3}$ \sqrt{3}

$\sqrt{x+y}$ \sqrt{x+y}

$\sqrt{x+\frac{1}{2}}$ \sqrt{x+\frac{1}{2}}

$\sqrt[3]{3}$ \sqrt[3]{3}

$\sqrt[n]{x}$ \sqrt[n]{x}

Sums, Products, Limits and Logarithms

Use the commands \sum, \prod, \lim, and \log respectively. To denote lower and upper bounds, or the base of the logarithm, use _ and ^ in the same way they are used for subscripts and superscripts. (Lower and upper bounds for integrals work the same way, as you'll see in the calculus section)

Symbol Command

$\textstyle \sum_{i=1}^{\infty}\frac{1}{i}$ \sum_{i=1}^{\infty}\frac{1}{i}

$\textstyle \prod_{n=1}^5\frac{n}{n-1}$ \prod_{n=1}^5\frac{n}{n-1}

$\textstyle \lim_{x\to\infty}\frac{1}{x}$ \lim_{x\to\infty}\frac{1}{x}

$\textstyle \lim\limits_{x\to\infty}\frac{1}{x}$ \lim\limits_{x\to\infty}\frac{1}{x}

$\textstyle \log_n n^2$ \log_n n^2

Some of these are prettier in display mode:

Symbol Command

$\sum_{i=1}^{\infty}\frac{1}{i}$ \sum_{i=1}^{\infty}\frac{1}{i}

$\prod_{n=1}^5\frac{n}{n-1}$ \prod_{n=1}^5\frac{n}{n-1}

$\lim_{x\to\infty}\frac{1}{x}$ \lim_{x\to\infty}\frac{1}{x}

Note that we can use sums, products, and logarithms without _ or ^ modifiers.

Symbol Command

$\sum\frac{1}{i}$ \sum\frac{1}{i}

$\frac{n}{n-1}$ \frac{n}{n-1}

$\textstyle \log n^2$ \log n^2

$\textstyle \ln e$ \ln e

Mods

Symbol Command

$9\equiv 3 \bmod{6}$ 9\equiv 3 \bmod{6}

$9\equiv 3 \pmod{6}$ 9\equiv 3 \pmod{6}

$9\equiv 3 \mod{6}$ 9\equiv 3 \mod{6}

$9\equiv 3\pod{6}$ 9\equiv 3 \pod{6}

Combinations

Symbol Command

$\scriptstyle\binom{1}{1}$ \binom{1}{1}

$\scriptstyle\binom{n-1}{r-1}$ \binom{n-1}{r-1}

These often look better in display mode:

Symbol Command

$\dbinom{9}{3}$ \dbinom{9}{3}

$\dbinom{n-1}{r-1}$ \dbinom{n-1}{r-1}