Mister Exam

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Sum of series:
(1)/((nlnn)(lnlnn)^2)
5/((5n-2)*(5n+3))
1/(2k+1)^2
((-1)^n)(pi^(2n))/((6^(2n))(2n)!)
Identical expressions
(one)/((nlnn)(lnlnn)^ two)
(1) divide by ((nlnn)(lnlnn) squared )
(one) divide by ((nlnn)(lnlnn) to the power of two)
(1)/((nlnn)(lnlnn)2)
1/nlnnlnlnn2
(1)/((nlnn)(lnlnn)²)
(1)/((nlnn)(lnlnn) to the power of 2)
1/nlnnlnlnn^2
(1) divide by ((nlnn)(lnlnn)^2)

Sum of series/ (1)/((nlnn)(lnlnn)^2)

Sum of series (1)/((nlnn)(lnlnn)^2)

The solution

You have entered [src]

  oo                       
____                       
\   `                      
 \              1          
  \   ---------------------
  /               2        
 /    n*log(n)*log (log(n))
/___,                      
n = 3

$$\sum_{n=3}^{\infty} \frac{1}{n \log{\left(n \right)} \log{\left(\log{\left(n \right)} \right)}^{2}}$$

Sum(1/((n*log(n))*log(log(n))^2), (n, 3, oo))

The rate of convergence of the power series

The answer [src]

  oo                       
____                       
\   `                      
 \              1          
  \   ---------------------
  /               2        
 /    n*log(n)*log (log(n))
/___,                      
n = 3

$$\sum_{n=3}^{\infty} \frac{1}{n \log{\left(n \right)} \log{\left(\log{\left(n \right)} \right)}^{2}}$$

Sum(1/(n*log(n)*log(log(n))^2), (n, 3, oo))

The graph

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

Sum of series (1)/((nlnn)(lnlnn)^2)

The solution

Examples of finding the sum of a series