Mister Exam

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Sum of series:
ln(1/n+2)
x^2/n^3
1/nln(n)(ln(ln(n)))^p
n*0,5^n
Identical expressions
one /nln(n)(ln(ln(n)))^p
1 divide by nln(n)(ln(ln(n))) to the power of p
one divide by nln(n)(ln(ln(n))) to the power of p
1/nln(n)(ln(ln(n)))p
1/nlnnlnlnnp
1/nlnnlnlnn^p
1 divide by nln(n)(ln(ln(n)))^p

Sum of series 1/nln(n)(ln(ln(n)))^p

The solution

You have entered [src]

  oo                     
 ___                     
 \  `                    
  \   log(n)    p        
   )  ------*log (log(n))
  /     n                
 /__,                    
n = 3

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

Sum((log(n)/n)*log(log(n))^p, (n, 3, oo))

The answer [src]

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

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

Sum(log(log(n))^p*log(n)/n, (n, 3, 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

Sum of series 1/nln(n)(ln(ln(n)))^p

The solution

Examples of finding the sum of a series