Mister Exam
Other calculators
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How to use it?
- Sum of series:
- (2^n+3^n)/6^n
- 1/n!
- x^n/2^n
- 1/(3n-2)*(3n+1)
-
Identical expressions
- (two ^n+ three ^n)/ six ^n
- (2 to the power of n plus 3 to the power of n) divide by 6 to the power of n
- (two to the power of n plus three to the power of n) divide by six to the power of n
- (2n+3n)/6n
- 2n+3n/6n
- 2^n+3^n/6^n
- (2^n+3^n) divide by 6^n
-
Similar expressions
- (2^n-3^n)/6^n
Sum of series (2^n+3^n)/6^n
The solution
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oo ____ \ ` \ n n \ 2 + 3 ) ------- / n / 6 /___, n = 1
$$\sum_{n=1}^{\infty} \frac{2^{n} + 3^{n}}{6^{n}}$$
Sum((2^n + 3^n)/6^n, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{2^{n} + 3^{n}}{6^{n}}$$
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
$$a_{n} = 2^{n} + 3^{n}$$
and
$$x_{0} = -6$$
,
$$d = -1$$
,
$$c = 0$$
then
$$\frac{1}{R} = \tilde{\infty} \left(-6 + \lim_{n \to \infty}\left(\frac{2^{n} + 3^{n}}{2^{n + 1} + 3^{n + 1}}\right)\right)$$
Let's take the limit
we find
$$R = 0$$
$$\frac{2^{n} + 3^{n}}{6^{n}}$$
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
$$a_{n} = 2^{n} + 3^{n}$$
and
$$x_{0} = -6$$
,
$$d = -1$$
,
$$c = 0$$
then
$$\frac{1}{R} = \tilde{\infty} \left(-6 + \lim_{n \to \infty}\left(\frac{2^{n} + 3^{n}}{2^{n + 1} + 3^{n + 1}}\right)\right)$$
Let's take the limit
we find
False
False
$$R = 0$$
The rate of convergence of the power series
The graph