Mister Exam

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Sum of series:
factorial(n)/(n^3+n^2+4)
ln(k/(k+1))
x/(x-1)
sin(n*x)/5^n
Identical expressions
sin(n*x)/ five ^n
sinus of (n multiply by x) divide by 5 to the power of n
sinus of (n multiply by x) divide by five to the power of n
sin(n*x)/5n
sinn*x/5n
sin(nx)/5^n
sin(nx)/5n
sinnx/5n
sinnx/5^n
sin(n*x) divide by 5^n

Sum of series/ sin(n*x)/5^n

Sum of series sin(n*x)/5^n

The solution

You have entered [src]

  oo          
____          
\   `         
 \    sin(n*x)
  \   --------
  /       n   
 /       5    
/___,         
n = 1

$$\sum_{n=1}^{\infty} \frac{\sin{\left(n x \right)}}{5^{n}}$$

Sum(sin(n*x)/5^n, (n, 1, oo))

The answer [src]

  oo              
 ___              
 \  `             
  \    -n         
  /   5  *sin(n*x)
 /__,             
n = 1

$$\sum_{n=1}^{\infty} 5^{- n} \sin{\left(n x \right)}$$

Sum(5^(-n)*sin(n*x), (n, 1, oo))

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
```