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Sum of series:
(3-2i-5i^2+8i^3)
log(1+1/n)/n
ln5
1/(n*ln^2n)
Identical expressions
(three - two i-5i^2+8i^ three)
(3 minus 2i minus 5i squared plus 8i cubed )
(three minus two i minus 5i squared plus 8i to the power of three)
(3-2i-5i2+8i3)
3-2i-5i2+8i3
(3-2i-5i²+8i³)
(3-2i-5i to the power of 2+8i to the power of 3)
3-2i-5i^2+8i^3
Similar expressions
(3-2i-5i^2-8i^3)
(3+2i-5i^2+8i^3)
(3-2i+5i^2+8i^3)

Sum of series/ (3-2i-5i^2+8i^3)

Sum of series (3-2i-5i^2+8i^3)

The solution

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  oo                         
 ___                         
 \  `                        
  \   /             2      3\
  /   \3 - 2*i - 5*i  + 8*i /
 /__,                        
i = 1

\sum_{i=1}^{\infty} \left(8 i^{3} + \left(- 5 i^{2} + \left(3 - 2 i\right)\right)\right)

Sum(3 - 2*i - 5*i^2 + 8*i^3, (i, 1, oo))

The radius of convergence of the power series

Given number:

8 i^{3} + \left(- 5 i^{2} + \left(3 - 2 i\right)\right)

It is a series of species

a_{i} \left(c x - x_{0}\right)^{d i}

- power series.
The radius of convergence of a power series can be calculated by the formula:

R^{d} = \frac{x_{0} + \lim_{i \to \infty} \left|{\frac{a_{i}}{a_{i + 1}}}\right|}{c}

In this case

a_{i} = 8 i^{3} - 5 i^{2} - 2 i + 3

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{i \to \infty}\left(\frac{\left|{8 i^{3} - 5 i^{2} - 2 i + 3}\right|}{- 2 i + 8 \left(i + 1\right)^{3} - 5 \left(i + 1\right)^{2} + 1}\right)

Let's take the limit
we find

True

False

The rate of convergence of the power series

The answer [src]

  oo                         
 ___                         
 \  `                        
  \   /       2            3\
  /   \3 - 5*i  - 2*i + 8*i /
 /__,                        
i = 1

\sum_{i=1}^{\infty} \left(8 i^{3} - 5 i^{2} - 2 i + 3\right)

Sum(3 - 5*i^2 - 2*i + 8*i^3, (i, 1, oo))

Numerical answer

The series diverges

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
```

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How to use it?

Identical expressions

Similar expressions

Sum of series (3-2i-5i^2+8i^3)

The solution

Examples of finding the sum of a series