$\text{Original & Alternating}$

$\begin{aligned} 1 + \dfrac12 + \dfrac13 + \dfrac14 + \dfrac15 + \dfrac16 + \dfrac17 + \dfrac18 + \dots &= \infty \\ 1 - \dfrac12 + \dfrac13 - \dfrac14 + \dfrac15 - \dfrac16 + \dfrac17 - \dfrac18 + \dots &= \ln2 \\ \\ 1 + \dfrac13 + \dfrac15 + \dfrac17 + \dfrac19 + \dfrac{1}{11} + \dfrac1{13} + \dfrac1{15} + \dots &= \infty \\ 1 - \dfrac13 + \dfrac15 - \dfrac17 + \dfrac19 - \dfrac{1}{11} + \dfrac1{13} - \dfrac1{15} + \dots &= \dfrac{\pi}{4} \\ \\ 1 + \dfrac12 + \dfrac14 + \dfrac18 + \dfrac1{16} + \dfrac{1}{32} + \dfrac1{64} + \dfrac1{128} + \dots &= 2 \\ 1 - \dfrac12 + \dfrac14 - \dfrac18 + \dfrac1{16} - \dfrac{1}{32} + \dfrac1{64} - \dfrac1{128} + \dots &= \dfrac23 \\ \\ 1 + \frac1{2^2} + \dfrac1{3^2} + \dfrac1{4^2} + \dfrac1{5^2} + \dfrac1{6^2} + \dfrac1{7^2} + \dfrac1{8^2} + \dots &= \dfrac{\pi^2}{6} \\ 1 - \frac1{2^2} + \dfrac1{3^2} - \dfrac1{4^2} + \dfrac1{5^2} - \dfrac1{6^2} + \dfrac1{7^2} - \dfrac1{8^2} + \dots &= \dfrac{\pi^2}{12} \\ \\ 1 + \frac1{2!} + \dfrac1{3!} + \dfrac1{4!} + \dfrac1{5!} + \dfrac1{6!} + \dfrac1{7!} + \dfrac1{8!} + \dots &= e - 1 \\ 1 - \frac1{2!} + \dfrac1{3!} - \dfrac1{4!} + \dfrac1{5!} - \dfrac1{6!} + \dfrac1{7!} - \dfrac1{8!} + \dots &= 1 - \dfrac1e \\ \\ 1 + \frac1{3!} + \dfrac1{5!} + \dfrac1{7!} + \dfrac1{9!} + \dfrac1{11!} + \dfrac1{13!} + \dfrac1{15!} + \dots &= \sinh1 \\ 1 - \frac1{3!} + \dfrac1{5!} - \dfrac1{7!} + \dfrac1{9!} - \dfrac1{11!} + \dfrac1{13!} - \dfrac1{15!} + \dots &= \sin1 \\ \\ 1 + \frac1{2!} + \dfrac1{4!} + \dfrac1{6!} + \dfrac1{8!} + \dfrac1{10!} + \dfrac1{12!} + \dfrac1{14!} + \dots &= \cosh1 \\ 1 - \frac1{2!} + \dfrac1{4!} - \dfrac1{6!} + \dfrac1{8!} - \dfrac1{10!} + \dfrac1{12!} - \dfrac1{14!} + \dots &= \cos1 \\ \\ 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + \dots &= \dfrac{-1}{12} \\ 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + \dots &= \dfrac{1}{4} \\ \end{aligned}$

$\text{Source: blackpen}\textcolor{#D61F06}{redpen}$

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

\(\text{Original & Alternating}\)

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