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Sum of series:
x^n/2^n
cos2n
sin(n+1/n)
nx^(n-1)
Identical expressions
x^n/ two ^n
x to the power of n divide by 2 to the power of n
x to the power of n divide by two to the power of n
xn/2n
x^n divide by 2^n

Sum of series x^n/2^n

The solution

You have entered [src]

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

$$\sum_{n=1}^{\infty} \frac{x^{n}}{2^{n}}$$

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

The answer [src]

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

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

Piecewise((x/(2*(1 - x/2)), |x|/2 < 1), (Sum(2^(-n)*x^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
```

Other calculators

How to use it?

Identical expressions

Sum of series x^n/2^n

The solution

Examples of finding the sum of a series