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Sum of series:
1/(4n^2-1)
1/(3n-2)*(3n+1)
1/ln(n)
x^n-x^(n-1)
Identical expressions
x^n-x^(n- one)
x to the power of n minus x to the power of (n minus 1)
x to the power of n minus x to the power of (n minus one)
xn-x(n-1)
xn-xn-1
x^n-x^n-1
Similar expressions
x^n+x^(n-1)
x^n-x^(n+1)

Sum of series x^n-x^(n-1)

The solution

You have entered [src]

  oo               
 ___               
 \  `              
  \   / n    n - 1\
  /   \x  - x     /
 /__,              
n = 2

$$\sum_{n=2}^{\infty} \left(x^{n} - x^{n - 1}\right)$$

Sum(x^n - x^(n - 1), (n, 2, oo))

The answer [src]

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

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

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

Similar expressions

Sum of series x^n-x^(n-1)

The solution

Examples of finding the sum of a series