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Sum of series:
1/(n(n+5))
1/(ln(x+2)*ln(x+2))
3^(-n)
cos(2*n)/n^2
Identical expressions
one /(ln(x+ two)*ln(x+ two))
1 divide by (ln(x plus 2) multiply by ln(x plus 2))
one divide by (ln(x plus two) multiply by ln(x plus two))
1/(ln(x+2)ln(x+2))
1/lnx+2lnx+2
1 divide by (ln(x+2)*ln(x+2))
Similar expressions
1/(ln(x-2)*ln(x+2))
1/(ln(x+2)*ln(x-2))

Sum of series 1/(ln(x+2)*ln(x+2))

The solution

You have entered [src]

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

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

Sum(1/(log(x + 2)*log(x + 2)), (n, 1, oo))

The radius of convergence of the power series

Given number:

\frac{1}{\log{\left(x + 2 \right)} \log{\left(x + 2 \right)}}

It is a series of species

a_{n} \left(c x - x_{0}\right)^{d n}

- power series.
The radius of convergence of a power series can be calculated by the formula:

R^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}

In this case

a_{n} = \frac{1}{\log{\left(x + 2 \right)}^{2}}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty} 1

Let's take the limit
we find

True

False

The answer [src]

     oo    
-----------
   2       
log (2 + x)

\frac{\infty}{\log{\left(x + 2 \right)}^{2}}

oo/log(2 + x)^2

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 1/(ln(x+2)*ln(x+2))

The solution

Examples of finding the sum of a series