Mister Exam

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Sum of series:
(n^2-3n-18)
2^(k+3)/5^(k+1)
2*n/(1+n^2)
1/9n^2-3n-2
Identical expressions
x^ two /((2x^ three +x)lnx)
x squared divide by ((2x cubed plus x)lnx)
x to the power of two divide by ((2x to the power of three plus x)lnx)
x2/((2x3+x)lnx)
x2/2x3+xlnx
x²/((2x³+x)lnx)
x to the power of 2/((2x to the power of 3+x)lnx)
x^2/2x^3+xlnx
x^2 divide by ((2x^3+x)lnx)
Similar expressions
x^2/((2x^3-x)lnx)

Sum of series x^2/((2x^3+x)lnx)

The solution

You have entered [src]

  5                    
____                   
\   `                  
 \             2       
  \           x        
   )  -----------------
  /   /   3    \       
 /    \2*x  + x/*log(x)
/___,                  
n = 2

$$\sum_{n=2}^{5} \frac{x^{2}}{\left(2 x^{3} + x\right) \log{\left(x \right)}}$$

Sum(x^2/(((2*x^3 + x)*log(x))), (n, 2, 5))

The answer [src]

          2      
       4*x       
-----------------
/       3\       
\x + 2*x /*log(x)

$$\frac{4 x^{2}}{\left(2 x^{3} + x\right) \log{\left(x \right)}}$$

4*x^2/((x + 2*x^3)*log(x))

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 x^2/((2x^3+x)lnx)

The solution

Examples of finding the sum of a series