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Sum of series:
(3^n-1)/n!
sin2n
(5^n-4^n)/6^n
2i
Derivative of:
x^(n+1)
Identical expressions
x^(n+ one)
x to the power of (n plus 1)
x to the power of (n plus one)
x(n+1)
xn+1
x^n+1
Similar expressions
x^(n-1)

Sum of series x^(n+1)

The solution

You have entered [src]

  oo        
 ___        
 \  `       
  \    n + 1
  /   x     
 /__,       
n = 0

$$\sum_{n=0}^{\infty} x^{n + 1}$$

Sum(x^(n + 1), (n, 0, oo))

The answer [src]

  //   1                 \
  || -----    for |x| < 1|
  || 1 - x               |
  ||                     |
  ||  oo                 |
x*|< ___                 |
  || \  `                |
  ||  \    n             |
  ||  /   x    otherwise |
  || /__,                |
  \\n = 0                /

$$x \left(\begin{cases} \frac{1}{1 - x} & \text{for}\: \left|{x}\right| < 1 \\\sum_{n=0}^{\infty} x^{n} & \text{otherwise} \end{cases}\right)$$

x*Piecewise((1/(1 - x), |x| < 1), (Sum(x^n, (n, 0, 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
```

Other calculators

How to use it?

Identical expressions

Similar expressions

Sum of series x^(n+1)

The solution

Examples of finding the sum of a series