Mister Exam
Other calculators
- Taylor Series Step by Step
- Fourier series step by step
- Differential equations Step by Step
- Product of series
-
How to use it?
- Sum of series:
- n^2*x^n/4^n
-
3/(8^(n-1))
- (3x)^2n/ln(2n-1)
-
(16-16cos(3(pi)n/4)/(pi^2n^2))cos(n(pi))
-
Identical expressions
- (three ^x+ two ^x)/x!
- (3 to the power of x plus 2 to the power of x) divide by x!
- (three to the power of x plus two to the power of x) divide by x!
- (3x+2x)/x!
- 3x+2x/x!
- 3^x+2^x/x!
- (3^x+2^x) divide by x!
-
Similar expressions
- (3^x-2^x)/x!
Sum of series (3^x+2^x)/x!
The solution
You have entered
[src]
oo ____ \ ` \ x x \ 3 + 2 / ------- / x! /___, n = 0
$$\sum_{n=0}^{\infty} \frac{2^{x} + 3^{x}}{x!}$$
Sum((3^x + 2^x)/factorial(x), (n, 0, oo))
The radius of convergence of the power series
Given number:
$$\frac{2^{x} + 3^{x}}{x!}$$
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
$$a_{n} = \frac{2^{x} + 3^{x}}{x!}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} 1$$
Let's take the limit
we find
$$\frac{2^{x} + 3^{x}}{x!}$$
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
$$a_{n} = \frac{2^{x} + 3^{x}}{x!}$$
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]
/ x x\
oo*\2 + 3 /
------------
x!
$$\frac{\infty \left(2^{x} + 3^{x}\right)}{x!}$$
oo*(2^x + 3^x)/factorial(x)
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