Sum of series 1/3n+23n+1

The solution

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 ___                
 \  `               
  \   /n           \
   )  |- + 23*n + 1|
  /   \3           /
 /__,               
n = 1

$$\sum_{n=1}^{\infty} \left(\left(\frac{n}{3} + 23 n\right) + 1\right)$$

Sum(n/3 + 23*n + 1, (n, 1, oo))

The radius of convergence of the power series

Given number:
$$\left(\frac{n}{3} + 23 n\right) + 1$$
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
$$a_{n} = \frac{70 n}{3} + 1$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\frac{70 n}{3} + 1}{\frac{70 n}{3} + \frac{73}{3}}\right)$$
Let's take the limit
we find

True

False

The rate of convergence of the power series

The answer [src]

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$$\infty$$

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Numerical answer

The series diverges

The graph

Examples of finding the sum of a series

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```
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```
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(-1)^(n + 1)/n
```
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```
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```
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```
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```
Exam the series for convergence
```
(3*n - 1)/(-5)^n
```

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Identical expressions

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Sum of series 1/3n+23n+1

The solution

Examples of finding the sum of a series