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:
- (-1)^nx^n/n!
- ((2*n+4)/(5*n+7))^n*x^n
-
(n-2^(3*n))/(n+1)^(1/3)
- (-1)^(2n+1)*x^(2n+1)/(2n+1)!
-
Identical expressions
- ((7n+ five)/(2n))^n
- ((7n plus 5) divide by (2n)) to the power of n
- ((7n plus five) divide by (2n)) to the power of n
- ((7n+5)/(2n))n
- 7n+5/2nn
- 7n+5/2n^n
- ((7n+5) divide by (2n))^n
-
Similar expressions
- ((7n-5)/(2n))^n
Sum of series ((7n+5)/(2n))^n
The solution
You have entered
[src]
oo ____ \ ` \ n \ /7*n + 5\ / |-------| / \ 2*n / /___, n = 1
$$\sum_{n=1}^{\infty} \left(\frac{7 n + 5}{2 n}\right)^{n}$$
Sum(((7*n + 5)/((2*n)))^n, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\left(\frac{7 n + 5}{2 n}\right)^{n}$$
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
$$a_{n} = \left(\frac{7 n + 5}{2 n}\right)^{n}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\left(\frac{7 n + 5}{2 n}\right)^{n} \left(\frac{7 n + 12}{2 \left(n + 1\right)}\right)^{- n - 1}\right)$$
Let's take the limit
we find
$$\left(\frac{7 n + 5}{2 n}\right)^{n}$$
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
$$a_{n} = \left(\frac{7 n + 5}{2 n}\right)^{n}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\left(\frac{7 n + 5}{2 n}\right)^{n} \left(\frac{7 n + 12}{2 \left(n + 1\right)}\right)^{- n - 1}\right)$$
Let's take the limit
we find
False
False
False
The rate of convergence of the power series
The answer
[src]
oo ____ \ ` \ n \ /5 + 7*n\ / |-------| / \ 2*n / /___, n = 1
$$\sum_{n=1}^{\infty} \left(\frac{7 n + 5}{2 n}\right)^{n}$$
Sum(((5 + 7*n)/(2*n))^n, (n, 1, oo))
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