Mister Exam

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Sum of series:
sh(x)
ln(k+1/k+2)
1/((2n-1)(2n-1))
(1-p)^(n-1)
Identical expressions
(one -p)^(n- one)
(1 minus p) to the power of (n minus 1)
(one minus p) to the power of (n minus one)
(1-p)(n-1)
1-pn-1
1-p^n-1
Similar expressions
(1-p)^(n+1)
(1+p)^(n-1)

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

The solution

You have entered [src]

  oo              
 ___              
 \  `             
  \          n - 1
  /   (1 - p)     
 /__,             
n = 1

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

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

The answer [src]

/    1 - p                       
|    -----       for |-1 + p| < 1
|      p                         
|                                
|  oo                            
< ___                            
| \  `                           
|  \          n                  
|  /   (1 - p)      otherwise    
| /__,                           
\n = 1                           
---------------------------------
              1 - p

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

Piecewise(((1 - p)/p, |-1 + p| < 1), (Sum((1 - p)^n, (n, 1, oo)), True))/(1 - p)

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 (1-p)^(n-1)

The solution

Examples of finding the sum of a series