Mister Exam
Other calculators
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How to use it?
- Sum of series:
- x^(2n)/n!
-
cos(n)/n
- cos(xi+yi)
-
(-1)n/2n-1
- Limit of the function:
-
cos(n)/n
- Graphing y =:
- cos(n)/n
-
Identical expressions
- cos(n)/n
- co sinus of e of (n) divide by n
- cosn/n
- cos(n) divide by n
-
Similar expressions
- (1-cosn)/n^4
- cosn/n
- (1-cosn)/(n^2+n-1)
- cos(n)/(n^(2/3)+1)
- (n+cosn)/((n^2)(sqrt(n)))
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Expressions with functions
- Cosine cos
- cos(xi+yi)
- cos(nx)/n^2
- cos(npi)/5^n
- cos(n)
- cos(n*100)/(n^2+1)
Sum of series cos(n)/n
The solution
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oo ___ \ ` \ cos(n) ) ------ / n /__, n = 1
$$\sum_{n=1}^{\infty} \frac{\cos{\left(n \right)}}{n}$$
Sum(cos(n)/n, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{\cos{\left(n \right)}}{n}$$
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
$$a_{n} = \frac{\cos{\left(n \right)}}{n}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\left(n + 1\right) \left|{\frac{\cos{\left(n \right)}}{\cos{\left(n + 1 \right)}}}\right|}{n}\right)$$
Let's take the limit
we find
$$\frac{\cos{\left(n \right)}}{n}$$
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
$$a_{n} = \frac{\cos{\left(n \right)}}{n}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\left(n + 1\right) \left|{\frac{\cos{\left(n \right)}}{\cos{\left(n + 1 \right)}}}\right|}{n}\right)$$
Let's take the limit
we find
True
False
The rate of convergence of the power series
Numerical answer
The series diverges
The graph