Mister Exam

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Sum of series:
1/(n(n+1))
(3^(n+3))/(4^(n-1)*5^n)
cosnx
0,5
Identical expressions
two n^ two (x+ two)^(n^2)
2n squared (x plus 2) to the power of (n squared )
two n to the power of two (x plus two) to the power of (n squared )
2n2(x+2)(n2)
2n2x+2n2
2n²(x+2)^(n²)
2n to the power of 2(x+2) to the power of (n to the power of 2)
2n^2x+2^n^2
Similar expressions
2n^2(x-2)^(n^2)

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

The solution

You have entered [src]

  oo                  
 ___                  
 \  `                 
  \               / 2\
   )     2        \n /
  /   2*n *(x + 2)    
 /__,                 
n = 1

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

Sum((2*n^2)*(x + 2)^(n^2), (n, 1, oo))

The answer [src]

  oo                  
 ___                  
 \  `                 
  \               / 2\
   )     2        \n /
  /   2*n *(2 + x)    
 /__,                 
n = 1

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

Sum(2*n^2*(2 + x)^(n^2), (n, 1, oo))

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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How to use it?

Identical expressions

Similar expressions

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

The solution

Examples of finding the sum of a series