Solving Taylor Series: Discover the Function Behind this Tricky Sequence

vucollegeguy
Messages
28
Reaction score
0

Homework Statement



What function produces the following:
(\pi2/(22)) - (\pi4/(24*3!)) + (\pi6/(26*5!)) - (\pi8/(28*7!))

I'm sure this is a sin function.
But I can't figure out what exactly is the function.

Please help.
 
Physics news on Phys.org
That can be written as

\pi/2[\pi/2 - (\pi/2)^3/3! + (\pi/2)^5/5! + ...]
 
Is that my final answer?
Or would sin(pi/2) be it?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Taylor Series for Square Root Function
Replies
18
Views
2K
Understanding and Solving the Taylor Series for a Specific Point
Replies
3
Views
1K
"How do I compute the Taylor series for cos(7x^2) at x=0?
Replies
15
Views
2K
Problem Involving Two-variable Taylor's Series
Replies
2
Views
2K
I Taylor series and variable substitutions
Replies
3
Views
2K
Complex Analysis - Taylor series of 1/(1+exp(z))
Replies
4
Views
6K
Taylor Series Help: Solving sin(x) Equation
Replies
7
Views
2K
What formula should be used to find the Fourier series of an even function?
Replies
1
Views
1K
Discover the Taylor Series for 3/(z-4i) about -5 | SOLVED
Replies
9
Views
5K
Finding a function from its MacLaurin series?
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top