Answers
Answer:
For inline formulas, enclose the formula in $...$. For displayed formulas, use $$...$$.
These render differently. For example, type
$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$
to show ∑
n
i=0
i2=
(n2+n)(2n+1)
6
(which is inline mode) or type
$$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$$
to show
n
∑
i=0 i2=
(n2+n)(2n+1)
6
(which is display mode).
For Greek letters, use \alpha, \beta, …, \omega: α,β,…ω. For uppercase, use \Gamma, \Delta, …, \Omega: Γ,Δ,…,Ω. Some Greek letters have variant forms: \epsilon \varepsilon ϵ, ε, \phi \varphi ϕ, φ, and others.
For superscripts and subscripts, use ^ and _. For example, x_i^2: x
2
i
, \log_2 x: log2x.
Groups. Superscripts, subscripts, and other operations apply only to the next “group”. A “group” is either a single symbol, or any formula surrounded by curly braces {…}. If you do 10^10, you will get a surprise: 1010. But 10^{10} gives what you probably wanted: 1010. Use curly braces to delimit a formula to which a superscript or subscript applies: x^5^6 is an error; {x^y}^z is xyz, and x^{y^z} is xyz. Observe the difference between x_i^2 x
2
i
and x_{i^2} xi2.
Parentheses Ordinary symbols ()[] make parentheses and brackets (2+3)[4+4]. Use \{ and \} for curly braces {}.
These do not scale with the formula in between, so if you write (\frac{\sqrt x}{y^3}) the parentheses will be too small: (
√
x
y3
). Using \left(…\right) will make the sizes adjust automatically to the formula they enclose: \left(\frac{\sqrt x}{y^3}\right) is (
√
x
y3
).
\left and\right apply to all the following sorts of parentheses: ( and ) (x), [ and ] [x], \{ and \} {x}, | |x|, \vert |x|, \Vert ‖x‖, \langle and \rangle ⟨x⟩, \lceil and \rceil ⌈x⌉, and \lfloor and \rfloor ⌊x⌋. \middle can be used to add additional dividers. There are also invisible parentheses, denoted by .: \left.\frac12\right\rbrace is
1
2
}.
If manual size adjustments are required: \Biggl(\biggl(\Bigl(\bigl((x)\bigr)\Bigr)\biggr)\Biggr) gives (((((x))))).
Answer:
udden udham jaisi Mikkelsen schhol still
think thankyou
Amit