Mister Exam

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Sum of series:
(5/6)^n
3i
sqrt(n^3+2)/(n^2+3)
(7^n-3^n)/21^n
Identical expressions
q^n*sin(na)
q to the power of n multiply by sinus of (na)
qn*sin(na)
qn*sinna
q^nsin(na)
qnsin(na)
qnsinna
q^nsinna

Sum of series/ q^n*sin(na)

Sum of series q^n*sin(na)

The solution

You have entered [src]

  oo             
 ___             
 \  `            
  \    n         
  /   q *sin(n*a)
 /__,            
n = 1

\sum_{n=1}^{\infty} q^{n} \sin{\left(a n \right)}

Sum(q^n*sin(n*a), (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
```