Mister Exam
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- Product of series
-
How to use it?
- Sum of series:
-
1/(3n-2)*(3n+1)
-
1/ln(n)
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14/(49n^2-70n-24)
- sqrt((k*x^2)/m)
-
Identical expressions
- fourteen /(49n^ two -70n- twenty-four)
- 14 divide by (49n squared minus 70n minus 24)
- fourteen divide by (49n to the power of two minus 70n minus twenty minus four)
- 14/(49n2-70n-24)
- 14/49n2-70n-24
- 14/(49n²-70n-24)
- 14/(49n to the power of 2-70n-24)
- 14/49n^2-70n-24
- 14 divide by (49n^2-70n-24)
-
Similar expressions
- 14/(49n^2-70n+24)
- 14/(49n^2+70n-24)
Sum of series 14/(49n^2-70n-24)
The solution
You have entered
[src]
oo ____ \ ` \ 14 \ ----------------- / 2 / 49*n - 70*n - 24 /___, n = 1
$$\sum_{n=1}^{\infty} \frac{14}{\left(49 n^{2} - 70 n\right) - 24}$$
Sum(14/(49*n^2 - 70*n - 24), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{14}{\left(49 n^{2} - 70 n\right) - 24}$$
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
$$a_{n} = \frac{14}{49 n^{2} - 70 n - 24}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(14 \left|{\frac{5 n - \frac{7 \left(n + 1\right)^{2}}{2} + \frac{47}{7}}{- 49 n^{2} + 70 n + 24}}\right|\right)$$
Let's take the limit
we find
$$\frac{14}{\left(49 n^{2} - 70 n\right) - 24}$$
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
$$a_{n} = \frac{14}{49 n^{2} - 70 n - 24}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(14 \left|{\frac{5 n - \frac{7 \left(n + 1\right)^{2}}{2} + \frac{47}{7}}{- 49 n^{2} + 70 n + 24}}\right|\right)$$
Let's take the limit
we find
True
False
The rate of convergence of the power series
The answer
[src]
7*Gamma(16/7) ------------- 30*Gamma(9/7)
$$\frac{7 \Gamma\left(\frac{16}{7}\right)}{30 \Gamma\left(\frac{9}{7}\right)}$$
7*gamma(16/7)/(30*gamma(9/7))
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