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Sum of series:
x^n/((3^n*n))
8760
-1/n^2
(-1)^k*(k-7)/(2*factorial(n-k))
Identical expressions
x^n/((three ^n*n))
x to the power of n divide by ((3 to the power of n multiply by n))
x to the power of n divide by ((three to the power of n multiply by n))
xn/((3n*n))
xn/3n*n
x^n/((3^nn))
xn/((3nn))
xn/3nn
x^n/3^nn
x^n divide by ((3^n*n))

Sum of series x^n/((3^n*n))

The solution

You have entered [src]

  oo      
____      
\   `     
 \      n 
  \    x  
   )  ----
  /    n  
 /    3 *n
/___,     
n = 1

$$\sum_{n=1}^{\infty} \frac{x^{n}}{3^{n} n}$$

Sum(x^n/((3^n*n)), (n, 1, oo))

The answer [src]

/    /    x\                          
|-log|1 - -|   for And(x >= -3, x < 3)
|    \    3/                          
|                                     
|  oo                                 
|____                                 
<\   `                                
| \     -n  n                         
|  \   3  *x                          
|  /   ------         otherwise       
| /      n                            
|/___,                                
\n = 1

$$\begin{cases} - \log{\left(1 - \frac{x}{3} \right)} & \text{for}\: x \geq -3 \wedge x < 3 \\\sum_{n=1}^{\infty} \frac{3^{- n} x^{n}}{n} & \text{otherwise} \end{cases}$$

Piecewise((-log(1 - x/3), (x >= -3)∧(x < 3)), (Sum(3^(-n)*x^n/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

Sum of series x^n/((3^n*n))

The solution

Examples of finding the sum of a series