Mister Exam

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Sum of series:
n^2*x^n
2(1/(n^2+5n+6))
cosn/n
(-1/2^(n+1))*(sen(n*a))
Identical expressions
n^ three *(x+ four)^(two *n- one)/factorial(n+ three)
n cubed multiply by (x plus 4) to the power of (2 multiply by n minus 1) divide by factorial(n plus 3)
n to the power of three multiply by (x plus four) to the power of (two multiply by n minus one) divide by factorial(n plus three)
n3*(x+4)(2*n-1)/factorial(n+3)
n3*x+42*n-1/factorialn+3
n³*(x+4)^(2*n-1)/factorial(n+3)
n to the power of 3*(x+4) to the power of (2*n-1)/factorial(n+3)
n^3(x+4)^(2n-1)/factorial(n+3)
n3(x+4)(2n-1)/factorial(n+3)
n3x+42n-1/factorialn+3
n^3x+4^2n-1/factorialn+3
n^3*(x+4)^(2*n-1) divide by factorial(n+3)
Similar expressions
n^3*(x-4)^(2*n-1)/factorial(n+3)
n^3*(x+4)^(2*n+1)/factorial(n+3)
n^3*(x+4)^(2*n-1)/factorial(n-3)

Sum of series/ n^3*(x+4)^(2*n-1)/factorial(n+3)

Sum of series n^3(x+4)^(2n-1)/factorial(n+3)

The solution

You have entered [src]

  oo                   
____                   
\   `                  
 \     3        2*n - 1
  \   n *(x + 4)       
  /   -----------------
 /         (n + 3)!    
/___,                  
n = 1

$$\sum_{n=1}^{\infty} \frac{n^{3} \left(x + 4\right)^{2 n - 1}}{\left(n + 3\right)!}$$

Sum((n^3*(x + 4)^(2*n - 1))/factorial(n + 3), (n, 1, oo))

The answer [src]

        /                                                                                       /       2\\
        |                4              2   /                  4             6              2\  \(4 + x) /|
        |648 + 12*(4 + x)  + 192*(4 + x)    \-648 - 144*(4 + x)  + 24*(4 + x)  + 456*(4 + x) /*e          |
(4 + x)*|-------------------------------- + --------------------------------------------------------------|
        |                   8                                                 8                           |
        \            (4 + x)                                           (4 + x)                            /
-----------------------------------------------------------------------------------------------------------
                                                     24

$$\frac{\left(x + 4\right) \left(\frac{12 \left(x + 4\right)^{4} + 192 \left(x + 4\right)^{2} + 648}{\left(x + 4\right)^{8}} + \frac{\left(24 \left(x + 4\right)^{6} - 144 \left(x + 4\right)^{4} + 456 \left(x + 4\right)^{2} - 648\right) e^{\left(x + 4\right)^{2}}}{\left(x + 4\right)^{8}}\right)}{24}$$

(4 + x)*((648 + 12*(4 + x)^4 + 192*(4 + x)^2)/(4 + x)^8 + (-648 - 144*(4 + x)^4 + 24*(4 + x)^6 + 456*(4 + x)^2)*exp((4 + x)^2)/(4 + x)^8)/24

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
```

Other calculators

How to use it?

Identical expressions

Similar expressions

Sum of series n^3*(x+4)^(2*n-1)/factorial(n+3)

The solution

Examples of finding the sum of a series

Sum of series n^3(x+4)^(2n-1)/factorial(n+3)