Mister Exam

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Sum of series:
3i
n^2*x^n
(n^3+n+5)/(n+2)
1/(1*3)+1/((2n-1)*(2n+1))
Identical expressions
a^(2n- one)/(2n- one)!
a to the power of (2n minus 1) divide by (2n minus 1)!
a to the power of (2n minus one) divide by (2n minus one)!
a(2n-1)/(2n-1)!
a2n-1/2n-1!
a^2n-1/2n-1!
a^(2n-1) divide by (2n-1)!
Similar expressions
a^(2n-1)/(2n+1)!
a^(2n+1)/(2n-1)!

Sum of series/ a^(2n-1)/(2n-1)!

Sum of series a^(2n-1)/(2n-1)!

The solution

You have entered [src]

  oo            
____            
\   `           
 \      2*n - 1 
  \    a        
  /   ----------
 /    (2*n - 1)!
/___,           
n = 1

$$\sum_{n=1}^{\infty} \frac{a^{2 n - 1}}{\left(2 n - 1\right)!}$$

Sum(a^(2*n - 1)/factorial(2*n - 1), (n, 1, oo))

The answer [src]

sinh(a)

$$\sinh{\left(a \right)}$$

sinh(a)

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
```