Mister Exam

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Sum of series:
n^2/3^n
1/((3*n+1)*(3*n+4))
sin(n*x)/n^2
sin²n/√n³+5
Identical expressions
- one (one -q^n)
minus 1(1 minus q to the power of n)
minus one (one minus q to the power of n)
-1(1-qn)
-11-qn
-11-q^n
Similar expressions
-1(1+q^n)
1(1-q^n)

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

The solution

You have entered [src]

  oo           
 ___           
 \  `          
  \    /     n\
  /   -\1 - q /
 /__,          
n = 1

$$\sum_{n=1}^{\infty} - (1 - q^{n})$$

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

The answer [src]

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

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

-oo + Piecewise((q/(1 - q), |q| < 1), (Sum(q^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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Identical expressions

Similar expressions

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

The solution

Examples of finding the sum of a series