Mister Exam

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Sum of series:
n^2*x^(n-1)
(n+1)/(n+3)-(n+2)/(n+4)
(2*n-3)/(n^2+2)
(0,0140-0,99)^2
Identical expressions
five thousand, seven hundred and thirteen ^(two *(x/ five thousand, seven hundred and thirteen))/(five thousand, seven hundred and thirteen + five thousand, seven hundred and thirteen ^(two *(x5712)))
5713 to the power of (2 multiply by (x divide by 5713)) divide by (5713 plus 5713 to the power of (2 multiply by (x5712)))
five thousand, seven hundred and thirteen to the power of (two multiply by (x 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 (two multiply by (x5712)))
5713(2*(x/5713))/(5713+5713(2*(x5712)))
57132*x/5713/5713+57132*x5712
5713^(2(x/5713))/(5713+5713^(2(x5712)))
5713(2(x/5713))/(5713+5713(2(x5712)))
57132x/5713/5713+57132x5712
5713^2x/5713/5713+5713^2x5712
5713^(2*(x divide by 5713)) divide by (5713+5713^(2*(x5712)))
Similar expressions
5713^(2*(x/5713))/(5713-5713^(2*(x5712)))

Sum of series/ 5713^(2*(x/5713))/(5713+5713^(2*(x5712)))

Sum of series 5713^(2(x/5713))/(5713+5713^(2(x5712)))

The solution

You have entered [src]

 5713                    
_____                    
\    `                   
 \                x      
  \            2*----    
   \             5713    
    )      5713          
   /   ------------------
  /               2*x5712
 /     5713 + 5713       
/____,                   
x = 0

$$\sum_{x=0}^{5713} \frac{5713^{2 \frac{x}{5713}}}{5713^{2 x_{5712}} + 5713}$$

Sum(5713^(2*(x/5713))/(5713 + 5713^(2*x5712)), (x, 0, 5713))

The answer [src]

                        2/5713       
       1 - 32638369*5713             
-------------------------------------
/        2/5713\ /           2*x5712\
\1 - 5713      /*\5713 + 5713       /

$$\frac{1 - 32638369 \cdot 5713^{\frac{2}{5713}}}{\left(1 - 5713^{\frac{2}{5713}}\right) \left(5713^{2 x_{5712}} + 5713\right)}$$

(1 - 32638369*5713^(2/5713))/((1 - 5713^(2/5713))*(5713 + 5713^(2*x5712)))

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^(2*(x/5713))/(5713+5713^(2*(x5712)))

The solution

Examples of finding the sum of a series

Sum of series 5713^(2(x/5713))/(5713+5713^(2(x5712)))