Mister Exam

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Sum of series:
1/n^3
1/((3n-2)*(3n+1))
1/(4n^2-9)
n*3^n+1
Integral of d{x}:
nx^(n-1)
Identical expressions
nx^(n- one)
nx to the power of (n minus 1)
nx to the power of (n minus one)
nx(n-1)
nxn-1
nx^n-1
Similar expressions
nx^(n+1)

Sum of series nx^(n-1)

The solution

You have entered [src]

  oo          
 ___          
 \  `         
  \      n - 1
  /   n*x     
 /__,         
n = 1

$$\sum_{n=1}^{\infty} n x^{n - 1}$$

Sum(n*x^(n - 1), (n, 1, oo))

The answer [src]

/    x                  
| --------   for |x| < 1
|        2              
| (1 - x)               
|                       
|  oo                   
< ___                   
| \  `                  
|  \      n             
|  /   n*x    otherwise 
| /__,                  
|n = 1                  
\                       
------------------------
           x

$$\frac{\begin{cases} \frac{x}{\left(1 - x\right)^{2}} & \text{for}\: \left|{x}\right| < 1 \\\sum_{n=1}^{\infty} n x^{n} & \text{otherwise} \end{cases}}{x}$$

Piecewise((x/(1 - x)^2, |x| < 1), (Sum(n*x^n, (n, 1, oo)), True))/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
```

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Identical expressions

Similar expressions

Sum of series nx^(n-1)

The solution

Examples of finding the sum of a series