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Sum of series:
1/(n*ln(n+1))
(-1)^n/3^n
(1-x^4)^n/(n+2)
1/((4n-3)*(4n+1))
Identical expressions
(one -x^ four)^n/(n+ two)
(1 minus x to the power of 4) to the power of n divide by (n plus 2)
(one minus x to the power of four) to the power of n divide by (n plus two)
(1-x4)n/(n+2)
1-x4n/n+2
(1-x⁴)^n/(n+2)
1-x^4^n/n+2
(1-x^4)^n divide by (n+2)
Similar expressions
(1+x^4)^n/(n+2)
(1-x^4)^n/(n-2)

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

The solution

You have entered [src]

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

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

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

The answer [src]

/                           /               /     2\                                                \                                                          
|                           |     3*(1 + x)*\1 + x /*(-1 + x)                                       |                                                          
|                           |-3 + ---------------------------        /            /     2\         \|                                                          
|         /     2\          |                  2                3*log\1 + (1 + x)*\1 + x /*(-1 + x)/|                                                          
|-(1 + x)*\1 + x /*(-1 + x)*|-------------------------------- + ------------------------------------|                                                          
|                           |                   2                                    3              |                                                          
|                           |         2 /     2\          2                3 /     2\          3    |                                                          
|                           \  (1 + x) *\1 + x / *(-1 + x)          (1 + x) *\1 + x / *(-1 + x)     /         /   /     4 ___       \     /      4 ___       \\
|-----------------------------------------------------------------------------------------------------  for Or\And\x <= \/ 2 , x > 0/, And\x >= -\/ 2 , x < 0//
|                                                  3                                                                                                           
<                                                                                                                                                              
|                                             oo                                                                                                               
|                                           ____                                                                                                               
|                                           \   `                                                                                                              
|                                            \            n                                                                                                    
|                                             \   /     4\                                                                                                     
|                                              )  \1 - x /                                                                     otherwise                       
|                                             /   ---------                                                                                                    
|                                            /      2 + n                                                                                                      
|                                           /___,                                                                                                              
\                                           n = 1

$$\begin{cases} - \frac{\left(x - 1\right) \left(x + 1\right) \left(x^{2} + 1\right) \left(\frac{\frac{3 \left(x - 1\right) \left(x + 1\right) \left(x^{2} + 1\right)}{2} - 3}{\left(x - 1\right)^{2} \left(x + 1\right)^{2} \left(x^{2} + 1\right)^{2}} + \frac{3 \log{\left(\left(x - 1\right) \left(x + 1\right) \left(x^{2} + 1\right) + 1 \right)}}{\left(x - 1\right)^{3} \left(x + 1\right)^{3} \left(x^{2} + 1\right)^{3}}\right)}{3} & \text{for}\: \left(x \leq \sqrt[4]{2} \wedge x > 0\right) \vee \left(x \geq - \sqrt[4]{2} \wedge x < 0\right) \\\sum_{n=1}^{\infty} \frac{\left(1 - x^{4}\right)^{n}}{n + 2} & \text{otherwise} \end{cases}$$

Piecewise((-(1 + x)*(1 + x^2)*(-1 + x)*((-3 + 3*(1 + x)*(1 + x^2)*(-1 + x)/2)/((1 + x)^2*(1 + x^2)^2*(-1 + x)^2) + 3*log(1 + (1 + x)*(1 + x^2)*(-1 + x))/((1 + x)^3*(1 + x^2)^3*(-1 + x)^3))/3, ((x > 0)∧(x <= 2^(1/4)))∨((x < 0)∧(x >= -2^(1/4)))), (Sum((1 - x^4)^n/(2 + n), (n, 1, oo)), True))

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 (1-x^4)^n/(n+2)

The solution

Examples of finding the sum of a series