Mister Exam

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Sum of series:
(n^3+n+5)/(n+2)
(0.15/0.05)^1.3
5/(25*n^2-5*n-6)
tan(sqrt(n)/(n^2+1))
Identical expressions
(zero . fifteen / zero . five)^ one . three
(0.15 divide by 0.05) to the power of 1.3
(zero . fifteen divide by zero . five) to the power of one . three
(0.15/0.05)1.3
0.15/0.051.3
0.15/0.05^1.3
(0.15 divide by 0.05)^1.3

Sum of series/ (0.15/0.05)^1.3

Sum of series (0.15/0.05)^1.3

The solution

You have entered [src]

  5               
_____             
\    `            
 \              13
  \             --
   \            10
   /   /   3   \  
  /    |-------|  
 /     \20*1/20/  
/____,            
i = 1

5 _____ \ ` \ 13 \ -- \ 10 / / 3 \ / |-------| / \20*1/20/ /____, i = 1

Sum((3/(20*(1/20)))^(13/10), (i, 1, 5))

The rate of convergence of the power series

The answer [src]

    3/10
15*3

$$15 \cdot 3^{\frac{3}{10}}$$

15*3^(3/10)

Numerical answer [src]

20.8558375547386401072788144192

20.8558375547386401072788144192

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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Identical expressions

Sum of series (0.15/0.05)^1.3

The solution

Examples of finding the sum of a series