Mister Exam
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- Taylor Series Step by Step
- Fourier series step by step
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- Product of series
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How to use it?
- Sum of series:
-
n^2/3^n
-
n^3/2^n
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(3/4)^n
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1/((2n-1)*(2n+1))
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Identical expressions
- zero , eight *(one hundred and one , forty-eight + five , forty-eight)* one hundred and thirty-nine * three hundred and two * ten ^- six
- 0,8 multiply by (101,48 plus 5,48) multiply by 139 multiply by 302 multiply by 10 to the power of minus 6
- zero , eight multiply by (one hundred and one , forty minus eight plus five , forty minus eight) multiply by one hundred and thirty minus nine multiply by three hundred and two multiply by ten to the power of minus six
- 0,8*(101,48+5,48)*139*302*10-6
- 0,8*101,48+5,48*139*302*10-6
- 0,8(101,48+5,48)13930210^-6
- 0,8(101,48+5,48)13930210-6
- 0,8101,48+5,4813930210-6
- 0,8101,48+5,4813930210^-6
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Similar expressions
- 0,8*(101,48+5,48)*139*302*10^+6
- 0,8*(101,48-5,48)*139*302*10^-6
Sum of series 0,8*(101,48+5,48)*139*302*10^-6
The solution
You have entered
[src]
oo ____ \ ` \ /2537 137\ \ 4*|---- + ---| ) \ 25 25/ / --------------*139*302*1.0e-6 / 5 /___, n = 1
$$\sum_{n=1}^{\infty} 1.0 \cdot 10^{-6} \cdot 302 \cdot 139 \frac{4 \left(\frac{137}{25} + \frac{2537}{25}\right)}{5}$$
Sum((((4*(2537/25 + 137/25)/5)*139)*302)*1.0e-6, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$1 \cdot 10^{-6} \cdot 302 \cdot 139 \frac{4 \left(\frac{137}{25} + \frac{2537}{25}\right)}{5}$$
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
$$a_{n} = 3.591973504$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} 1$$
Let's take the limit
we find
$$1 \cdot 10^{-6} \cdot 302 \cdot 139 \frac{4 \left(\frac{137}{25} + \frac{2537}{25}\right)}{5}$$
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
$$a_{n} = 3.591973504$$
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 rate of convergence of the power series
The graph
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