Mister Exam

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Sum of series:
(n-1)/2^(n+1)
x^n/4^n
ln(n^3)/n^3+1
cos(a*n/2)/2^n
Identical expressions
x^n/ four ^n
x to the power of n divide by 4 to the power of n
x to the power of n divide by four to the power of n
xn/4n
x^n divide by 4^n

Sum of series x^n/4^n

The solution

You have entered [src]

  oo    
____    
\   `   
 \     n
  \   x 
   )  --
  /    n
 /    4 
/___,   
n = 1

$$\sum_{n=1}^{\infty} \frac{x^{n}}{4^{n}}$$

Sum(x^n/4^n, (n, 1, oo))

The answer [src]

/     x            |x|    
| ---------    for --- < 1
|   /    x\         4     
| 4*|1 - -|               
|   \    4/               
|                         
<  oo                     
| ___                     
| \  `                    
|  \    -n  n             
|  /   4  *x    otherwise 
| /__,                    
\n = 1

$$\begin{cases} \frac{x}{4 \left(1 - \frac{x}{4}\right)} & \text{for}\: \frac{\left|{x}\right|}{4} < 1 \\\sum_{n=1}^{\infty} 4^{- n} x^{n} & \text{otherwise} \end{cases}$$

Piecewise((x/(4*(1 - x/4)), |x|/4 < 1), (Sum(4^(-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/4^n

The solution

Examples of finding the sum of a series