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  • Sum of series:
  • 1/(n(n+1)) 1/(n(n+1))
  • ((2*n+4)/(5*n+7))^n*x^n
  • 2^2 2^2
  • (3^(n+3))/(4^(n-1)*5^n) (3^(n+3))/(4^(n-1)*5^n)

  • Identical expressions

  • ((two *n+ four)/(five *n+ seven))^n*x^n
  • ((2 multiply by n plus 4) divide by (5 multiply by n plus 7)) to the power of n multiply by x to the power of n
  • ((two multiply by n plus four) divide by (five multiply by n plus seven)) to the power of n multiply by x to the power of n
  • ((2*n+4)/(5*n+7))n*xn
  • 2*n+4/5*n+7n*xn
  • ((2n+4)/(5n+7))^nx^n
  • ((2n+4)/(5n+7))nxn
  • 2n+4/5n+7nxn
  • 2n+4/5n+7^nx^n
  • ((2*n+4) divide by (5*n+7))^n*x^n

  • Similar expressions

  • ((2*n+4)/(5*n-7))^n*x^n
  • ((2*n-4)/(5*n+7))^n*x^n
Sum of series/ ((2*n+4)/(5*n+7))^n*x^n

Sum of series ((2*n+4)/(5*n+7))^n*x^n


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The solution

You have entered [src] 
  oo               
____               
\   `              
 \             n   
  \   /2*n + 4\   n
  /   |-------| *x 
 /    \5*n + 7/    
/___,              
n = 1
$$\sum_{n=1}^{\infty} x^{n} \left(\frac{2 n + 4}{5 n + 7}\right)^{n}$$ 
Sum(((2*n + 4)/(5*n + 7))^n*x^n, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$x^{n} \left(\frac{2 n + 4}{5 n + 7}\right)^{n}$$
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
$$a_{n} = \left(\frac{2 n + 4}{5 n + 7}\right)^{n}$$
and
$$x_{0} = 0$$
,
$$d = 1$$
,
$$c = 1$$
then
$$R = \lim_{n \to \infty}\left(\left(\frac{2 n + 4}{5 n + 7}\right)^{n} \left(\frac{2 n + 6}{5 n + 12}\right)^{- n - 1}\right)$$
Let's take the limit
we find
$$R = \frac{5}{2}$$

    Examples of finding the sum of a series

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