Mister Exam
Other calculators
- Taylor Series Step by Step
- Fourier series step by step
- Differential equations Step by Step
- Product of series
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How to use it?
- Sum of series:
- t^k*(-1)^k*a^(2*k)*cos(a*x)*e^(a*z)/factorial(k)
- (-1)^nx^n/n!
-
5/(25*n^2-5*n-6)
- ((3*x)^n)/n!
-
Identical expressions
- y-cos(k*x)^ three
- y minus co sinus of e of (k multiply by x) cubed
- y minus co sinus of e of (k multiply by x) to the power of three
- y-cos(k*x)3
- y-cosk*x3
- y-cos(k*x)³
- y-cos(k*x) to the power of 3
- y-cos(kx)^3
- y-cos(kx)3
- y-coskx3
- y-coskx^3
-
Similar expressions
- y+cos(k*x)^3
Sum of series y-cos(k*x)^3
The solution
You have entered
[src]
oo ___ \ ` \ / 3 \ / \y - cos (k*x)/ /__, n = 1
$$\sum_{n=1}^{\infty} \left(y - \cos^{3}{\left(k x \right)}\right)$$
Sum(y - cos(k*x)^3, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$y - \cos^{3}{\left(k x \right)}$$
It is a series of species
$$a_{n} \left(c x - x_{0}\right)^{d n}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}$$
In this case
$$a_{n} = y - \cos^{3}{\left(k x \right)}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} 1$$
Let's take the limit
we find
$$y - \cos^{3}{\left(k x \right)}$$
It is a series of species
$$a_{n} \left(c x - x_{0}\right)^{d n}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}$$
In this case
$$a_{n} = y - \cos^{3}{\left(k x \right)}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} 1$$
Let's take the limit
we find
True
False
The answer
[src]
/ 3 \ oo*\y - cos (k*x)/
$$\infty \left(y - \cos^{3}{\left(k x \right)}\right)$$
oo*(y - cos(k*x)^3)
Examples of finding the sum of a series
- The Sum of the Power Series
x^n/n
(x-1)^n
- Factorial
1/2^(n!)
n^2/n!
x^n/n!
k!/(n!*(n+k)!)
- Flint Hills Series
csc(n)^2/n^3
- Basel problem
1/n^2
1/n^4
1/n^6
- Harmonic series
1/n
- Grandi's series
(-1)^n
- Alternating series
(-1)^(n + 1)/n
(n + 2)*(-1)^(n - 1)
(3*n - 1)/(-5)^n
(-1)^(n - 1)*n/(6*n - 5)
- Newton–Mercator series
(-1)^(n + 1)/n*x^n
- Exam the series for convergence
(3*n - 1)/(-5)^n