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Sum of series:
sin(3n)/(7n)^(1/5)
arctg1/(2n^2)
cos(i*n)/2^n
1/(n*ln(n)*(ln(ln(n)))^2)
Identical expressions
one /(k+ two)^ one / two
1 divide by (k plus 2) to the power of 1 divide by 2
one divide by (k plus two) to the power of one divide by two
1/(k+2)1/2
1/k+21/2
1/k+2^1/2
1 divide by (k+2)^1 divide by 2
Similar expressions
1/(k-2)^1/2

Sum of series 1/(k+2)^1/2

The solution

You have entered [src]

  oo           
____           
\   `          
 \        1    
  \   ---------
  /     _______
 /    \/ k + 2 
/___,          
n = 1

$$\sum_{n=1}^{\infty} \frac{1}{\sqrt{k + 2}}$$

Sum(1/(sqrt(k + 2)), (n, 1, oo))

The radius of convergence of the power series

Given number:
$$\frac{1}{\sqrt{k + 2}}$$
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
$$a_{n} = \frac{1}{\sqrt{k + 2}}$$
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 + k

$$\frac{\infty}{\sqrt{k + 2}}$$

oo/sqrt(2 + k)

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/(k+2)^1/2

The solution

Examples of finding the sum of a series