Mister Exam

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Sum of series/ senh(9ix)

Sum of series senh(9ix)

The solution

You have entered [src]

  oo             
 __              
 \ `             
  )   sinh(9*i*x)
 /_,             
i = 1

$$\sum_{i=1}^{\infty} \sinh{\left(9 i x \right)}$$

Sum(sinh((9*i)*x), (i, 1, oo))

The answer [src]

  oo             
 __              
 \ `             
  )   sinh(9*i*x)
 /_,             
i = 1

$$\sum_{i=1}^{\infty} \sinh{\left(9 i x \right)}$$

Sum(sinh(9*i*x), (i, 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
```