Mister Exam
Other calculators
- Taylor Series Step by Step
- Fourier series step by step
- Differential equations Step by Step
- Product of series
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How to use it?
- Sum of series:
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sin(3n)/(7n)^(1/5)
-
arctg1/(2n^2)
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cos(i*n)/2^n
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1/(n*ln(n)*(ln(ln(n)))^2)
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Identical expressions
- ln(n+ two)/n* one /(3n+ seven)^ one / two
- ln(n plus 2) divide by n multiply by 1 divide by (3n plus 7) to the power of 1 divide by 2
- ln(n plus two) divide by n multiply by one divide by (3n plus seven) to the power of one divide by two
- ln(n+2)/n*1/(3n+7)1/2
- lnn+2/n*1/3n+71/2
- ln(n+2)/n1/(3n+7)^1/2
- ln(n+2)/n1/(3n+7)1/2
- lnn+2/n1/3n+71/2
- lnn+2/n1/3n+7^1/2
- ln(n+2) divide by n*1 divide by (3n+7)^1 divide by 2
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Similar expressions
- ln(n-2)/n*1/(3n+7)^1/2
- ln(n+2)/n*1/(3n-7)^1/2
Sum of series ln(n+2)/n*1/(3n+7)^1/2
The solution
You have entered
[src]
oo _____ \ ` \ /log(n + 2)\ \ |----------| \ \ n / / ------------ / _________ / \/ 3*n + 7 /____, n = 1
$$\sum_{n=1}^{\infty} \frac{\frac{1}{n} \log{\left(n + 2 \right)}}{\sqrt{3 n + 7}}$$
Sum((log(n + 2)/n)/sqrt(3*n + 7), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{\frac{1}{n} \log{\left(n + 2 \right)}}{\sqrt{3 n + 7}}$$
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
$$a_{n} = \frac{\log{\left(n + 2 \right)}}{n \sqrt{3 n + 7}}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\left(n + 1\right) \sqrt{3 n + 10} \log{\left(n + 2 \right)}}{n \sqrt{3 n + 7} \log{\left(n + 3 \right)}}\right)$$
Let's take the limit
we find
$$\frac{\frac{1}{n} \log{\left(n + 2 \right)}}{\sqrt{3 n + 7}}$$
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
$$a_{n} = \frac{\log{\left(n + 2 \right)}}{n \sqrt{3 n + 7}}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\left(n + 1\right) \sqrt{3 n + 10} \log{\left(n + 2 \right)}}{n \sqrt{3 n + 7} \log{\left(n + 3 \right)}}\right)$$
Let's take the limit
we find
True
False
The rate of convergence of the power series
The answer
[src]
oo ____ \ ` \ log(2 + n) \ ------------- / _________ / n*\/ 7 + 3*n /___, n = 1
$$\sum_{n=1}^{\infty} \frac{\log{\left(n + 2 \right)}}{n \sqrt{3 n + 7}}$$
Sum(log(2 + n)/(n*sqrt(7 + 3*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