Mister Exam

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Sum of series:
x^(n-1)
0.5^(n)
(4^(n+1)-10^n)/20^n
1/((2n-1)(2n+5))
Derivative of:
x^(n-1)
Integral of d{x}:
x^(n-1)
Identical expressions
x^(n- one)
x to the power of (n minus 1)
x to the power of (n minus 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 = 1

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

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

The answer [src]

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

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

Piecewise((x/(1 - x), |x| < 1), (Sum(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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How to use it?

Identical expressions

Similar expressions

Sum of series x^(n-1)

The solution

Examples of finding the sum of a series