Mister Exam

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How to use it?
Sum of series:
(3^n-4^n)/12^n
2i
(4*9^n-2^n)/18^n
((-1)^(n+2)*4^n+5^(n+1))/7^(n-2)
Identical expressions
ln(5k/n)
ln(5k divide by n)
ln5k/n
Similar expressions
ln5k/n

Sum of series/ ln(5k/n)

Sum of series ln(5k/n)

The solution

You have entered [src]

  n           
 ___          
 \  `         
  \      /5*k\
   )  log|---|
  /      \ n /
 /__,         
k = 1

$$\sum_{k=1}^{n} \log{\left(\frac{5 k}{n} \right)}$$

Sum(log((5*k)/n), (k, 1, n))

The answer [src]

  n           
 ___          
 \  `         
  \      /5*k\
   )  log|---|
  /      \ n /
 /__,         
k = 1

$$\sum_{k=1}^{n} \log{\left(\frac{5 k}{n} \right)}$$

Sum(log(5*k/n), (k, 1, n))

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
```