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:
-
9/(9n^2+3n-20)
-
0.5^n
-
56724.3*10^-1
- 1/(sqrt(k^4+7k^2+20))
- Integral of d{x}:
- 3x+2x^2
-
Identical expressions
- 3x+ two x^2
- 3x plus 2x squared
- 3x plus two x squared
- 3x+2x2
- 3x+2x²
- 3x+2x to the power of 2
-
Similar expressions
- 3x-2x^2
Sum of series 3x+2x^2
The solution
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oo ___ \ ` \ / 2\ / \3*x + 2*x / /__, n = 1
$$\sum_{n=1}^{\infty} \left(2 x^{2} + 3 x\right)$$
Sum(3*x + 2*x^2, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$2 x^{2} + 3 x$$
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
$$a_{n} = 2 x^{2} + 3 x$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} 1$$
Let's take the limit
we find
$$2 x^{2} + 3 x$$
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
$$a_{n} = 2 x^{2} + 3 x$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} 1$$
Let's take the limit
we find
True
False
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