Mister Exam

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Sum of series:
1/(n^2-3n+2)
factorial(6*n)/(n-1)
5/n^2
sin^2((n^4+5)/(n^5+4))
Identical expressions
factorial(n)*x^n/ two ^n
factorial(n) multiply by x to the power of n divide by 2 to the power of n
factorial(n) multiply by x to the power of n divide by two to the power of n
factorial(n)*xn/2n
factorialn*xn/2n
factorial(n)x^n/2^n
factorial(n)xn/2n
factorialnxn/2n
factorialnx^n/2^n
factorial(n)*x^n divide by 2^n

Sum of series/ factorial(n)*x^n/2^n

Sum of series factorial(n)*x^n/2^n

The solution

You have entered [src]

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

$$\sum_{n=1}^{\infty} \frac{x^{n} n!}{2^{n}}$$

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

The answer [src]

  oo           
 ___           
 \  `          
  \    -n  n   
  /   2  *x *n!
 /__,          
n = 1

$$\sum_{n=1}^{\infty} 2^{- n} x^{n} n!$$

Sum(2^(-n)*x^n*factorial(n), (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
```