Mister Exam

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Sum of series:
3/(n*(n+2))
1/(n+1)!
nx^(n+1)
(-1)^n*x^(n+1)/factorial(n+1)
Identical expressions
nx^(n+ one)
nx to the power of (n plus 1)
nx to the power of (n plus 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                   |
x*|< ___                   |
  || \  `                  |
  ||  \      n             |
  ||  /   n*x    otherwise |
  || /__,                  |
  ||n = 1                  |
  \\                       /

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

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

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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How to use it?

Identical expressions

Similar expressions

Sum of series nx^(n+1)

The solution

Examples of finding the sum of a series