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oo ___ \ ` \ 1 ) - / n /__, n = 1

$$\sum_{n=1}^{\infty} \frac{1}{n}$$

Sum(1/n, (n, 1, oo))

The radius of convergence of the power series

Given number:

$$\frac{1}{n}$$

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

$$a_{n} = \frac{1}{n}$$

and

$$x_{0} = 0$$

,

$$d = 0$$

,

$$c = 1$$

then

$$1 = \lim_{n \to \infty}\left(\frac{n + 1}{n}\right)$$

Let's take the limit

we find

$$\frac{1}{n}$$

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

$$a_{n} = \frac{1}{n}$$

and

$$x_{0} = 0$$

,

$$d = 0$$

,

$$c = 1$$

then

$$1 = \lim_{n \to \infty}\left(\frac{n + 1}{n}\right)$$

Let's take the limit

we find

True

False

The rate of convergence of the power series

Numerical answer

The series diverges

The graph