Proving Maclaurin Series

Maclaurin series is very efficient and used to obtain and series even
The famous binomial theorem can be obtain from this
So let's get started PRÓOVE
IF, F(X)=A+BX+CX²+DX³+ EX⁴+…
F(0)=A
F'(0)=B
F''(0)=2C
HENCE,C=F''(0)/2!
F'''(0)=6D
SO,D=F'''(0)/3!
F''''(0)=24E
SO,E=F''''(0)/4!
Therefore,F(X)=F(0)+F'(0).X+F''(0)/2!.X²+F'''(0)/3!.X³+F''''(0)/4!.X⁴+... F^n(0)/n!.X^n
Hence the above is Maclaurin series

#Calculus

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

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}`	$\boxed{123}$

Comments

Sort by:

Top Newest

So I will some body to prove since using the series above

oluwadamilare prosper Adebola - 4 months, 2 weeks ago

I mean use the series to get since,cosx?

oluwadamilare prosper Adebola - 4 months, 2 weeks ago

That is hundred percent true I too have observed it and the funny thing about it is that it is what Srinivasa Ramanujan used it to prove his Master Theorem.

Aruna Yumlembam - 4 months, 2 weeks ago

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}`	$\boxed{123}$