Mister Exam

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Sum of series:
2-3(0.8)^n
(n+1)^n/(n^(n+2))
(3*n/(9*n-1))^n
(ln(n)/n)^p
Identical expressions
(ln(n)/n)^p
(ln(n) divide by n) to the power of p
(ln(n)/n)p
lnn/np
lnn/n^p
(ln(n) divide by n)^p

Sum of series/ (ln(n)/n)^p

Sum of series (ln(n)/n)^p

The solution

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  oo           
____           
\   `          
 \            p
  \   /log(n)\ 
  /   |------| 
 /    \  n   / 
/___,          
n = 1

$$\sum_{n=1}^{\infty} \left(\frac{\log{\left(n \right)}}{n}\right)^{p}$$

Sum((log(n)/n)^p, (n, 1, oo))

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
```