Mister Exam

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Sum of series:
ln^n(x)/n!
1/(n+6)(n+7)
(-1)^(n+1)/log(n+2^0.5)
x^(n-1)
Identical expressions
ln^n(x)/n!
ln to the power of n(x) divide by n!
lnn(x)/n!
lnnx/n!
ln^nx/n!
ln^n(x) divide by n!

Sum of series/ ln^n(x)/n!

Sum of series ln^n(x)/n!

The solution

You have entered [src]

  oo         
____         
\   `        
 \       n   
  \   log (x)
  /   -------
 /       n!  
/___,        
n = 1

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

Sum(log(x)^n/factorial(n), (n, 1, oo))

The answer [src]

/    1        x   \       
|- ------ + ------|*log(x)
\  log(x)   log(x)/

$$\left(\frac{x}{\log{\left(x \right)}} - \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}$$

(-1/log(x) + x/log(x))*log(x)

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
```