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Sum of series:
sin((n^2+3)/(n^3+2))^2
sin(nx)*(5-(3*n))
(n-1)*5
factorial(n)^2/factorial(k^n)
Identical expressions
sin(nx)*(five -(three *n))
sinus of (nx) multiply by (5 minus (3 multiply by n))
sinus of (nx) multiply by (five minus (three multiply by n))
sin(nx)(5-(3n))
sinnx5-3n
Similar expressions
sin(nx)*(5+(3*n))

Sum of series/ sin(nx)*(5-(3*n))

Sum of series sin(nx)(5-(3n))

The solution

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  oo                    
 __                     
 \ `                    
  )   sin(n*x)*(5 - 3*n)
 /_,                    
n = 0

$$\sum_{n=0}^{\infty} \left(5 - 3 n\right) \sin{\left(n x \right)}$$

Sum(sin(n*x)*(5 - 3*n), (n, 0, 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
```