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Sum of series:
9/(9n^2+3n-20)
0.5^n
56724.3*10^-1
1/(sqrt(k^4+7k^2+20))
Identical expressions
five thousand, seven hundred and thirteen ^(2n/ five thousand, seven hundred and thirteen)/ five thousand, seven hundred and thirteen + five thousand, seven hundred and thirteen ^(2x/ five thousand, seven hundred and thirteen)
5713 to the power of (2n divide by 5713) divide by 5713 plus 5713 to the power of (2x divide by 5713)
five thousand, seven hundred and thirteen to the power of (2n divide by five thousand, seven hundred and thirteen) divide by five thousand, seven hundred and thirteen plus five thousand, seven hundred and thirteen to the power of (2x divide by five thousand, seven hundred and thirteen)
5713(2n/5713)/5713+5713(2x/5713)
57132n/5713/5713+57132x/5713
5713^2n/5713/5713+5713^2x/5713
5713^(2n divide by 5713) divide by 5713+5713^(2x divide by 5713)
Similar expressions
5713^(2n/5713)/5713-5713^(2x/5713)

Sum of series/ 5713^(2n/5713)/5713+5713^(2x/5713)

Sum of series 5713^(2n/5713)/5713+5713^(2x/5713)

The solution

You have entered [src]

 5713                       
_____                       
\    `                      
 \     /    2*n            \
  \    |    ----       2*x |
   \   |    5713       ----|
   /   |5713           5713|
  /    |-------- + 5713    |
 /     \  5713             /
/____,                      
n = 0

$$\sum_{n=0}^{5713} \left(\frac{5713^{\frac{2 n}{5713}}}{5713} + 5713^{\frac{2 x}{5713}}\right)$$

Sum(5713^((2*n)/5713)/5713 + 5713^((2*x)/5713), (n, 0, 5713))

The answer [src]

         2*x                           
         ----                    2/5713
         5713   1 - 32638369*5713      
5714*5713     + -----------------------
                      /        2/5713\ 
                 5713*\1 - 5713      /

$$5714 \cdot 5713^{\frac{2 x}{5713}} + \frac{1 - 32638369 \cdot 5713^{\frac{2}{5713}}}{5713 \left(1 - 5713^{\frac{2}{5713}}\right)}$$

5714*5713^(2*x/5713) + (1 - 32638369*5713^(2/5713))/(5713*(1 - 5713^(2/5713)))

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
```

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Identical expressions

Similar expressions

Sum of series 5713^(2n/5713)/5713+5713^(2x/5713)

The solution

Examples of finding the sum of a series