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(n-1)*((6!)/((n!)*((6-n)!)))*(0,21^n*n!)/(1!*1^(6-n))*(0,174)

  • How to use it?

  • Sum of series:
  • 1/n! 1/n!
  • (1+sin(x))/n
  • 1/4n^2+1 1/4n^2+1
  • 1/(10^(4n-1)) 1/(10^(4n-1))

  • Identical expressions

  • (n- one)*((six !)/((n!)*((six -n)!)))*(zero , twenty-one ^n*n!)/(one !* one ^(six -n))*(zero , one hundred and seventy-four)
  • (n minus 1) multiply by ((6!) divide by ((n!) multiply by ((6 minus n)!))) multiply by (0,21 to the power of n multiply by n!) divide by (1! multiply by 1 to the power of (6 minus n)) multiply by (0,174)
  • (n minus one) multiply by ((six !) divide by ((n!) multiply by ((six minus n)!))) multiply by (zero , twenty minus one to the power of n multiply by n!) divide by (one ! multiply by one to the power of (six minus n)) multiply by (zero , one hundred and seventy minus four)
  • (n-1)*((6!)/((n!)*((6-n)!)))*(0,21n*n!)/(1!*1(6-n))*(0,174)
  • n-1*6!/n!*6-n!*0,21n*n!/1!*16-n*0,174
  • (n-1)((6!)/((n!)((6-n)!)))(0,21^nn!)/(1!1^(6-n))(0,174)
  • (n-1)((6!)/((n!)((6-n)!)))(0,21nn!)/(1!1(6-n))(0,174)
  • n-16!/n!6-n!0,21nn!/1!16-n0,174
  • n-16!/n!6-n!0,21^nn!/1!1^6-n0,174
  • (n-1)*((6!) divide by ((n!)*((6-n)!)))*(0,21^n*n!) divide by (1!*1^(6-n))*(0,174)

  • Similar expressions

  • (n-1)*((6!)/((n!)*((6+n)!)))*(0,21^n*n!)/(1!*1^(6-n))*(0,174)
  • (n-1)*((6!)/((n!)*((6-n)!)))*(0,21^n*n!)/(1!*1^(6+n))*(0,174)
  • (n+1)*((6!)/((n!)*((6-n)!)))*(0,21^n*n!)/(1!*1^(6-n))*(0,174)
Sum of series/ (n-1)*((6!)/((n!)*((6-n)!)))*(0,21^n*n!)/(1!*1^(6-n))*(0,174)

Sum of series (n-1)*((6!)/((n!)*((6-n)!)))*(0,21^n*n!)/(1!*1^(6-n))*(0,174)


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The solution

You have entered [src] 
   oo                                   
______                                  
\     `                                 
 \                               n      
  \                  6!     / 21\       
   \    (n - 1)*-----------*|---| *n!   
    \           n!*(6 - n)! \100/       
     )  -----------------------------*87
    /                 6 - n             
   /              1!*1                  
  /     --------------------------------
 /                    500               
/_____,                                 
 n = 2
$$\sum_{n=2}^{\infty} \frac{87 \frac{\left(\frac{21}{100}\right)^{n} n! \frac{6!}{n! \left(6 - n\right)!} \left(n - 1\right)}{1^{6 - n} 1!}}{500}$$ 
Sum(((((n - 1)*(factorial(6)/((factorial(n)*factorial(6 - n)))))*((21/100)^n*factorial(n)))/((factorial(1)*1^(6 - n))))*87/500, (n, 2, oo))
The radius of convergence of the power series
Given number:
$$\frac{87 \frac{\left(\frac{21}{100}\right)^{n} n! \frac{6!}{n! \left(6 - n\right)!} \left(n - 1\right)}{1^{6 - n} 1!}}{500}$$
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
$$a_{n} = \frac{3132 \left(n - 1\right)}{25 \left(6 - n\right)!}$$
and
$$x_{0} = - \frac{21}{100}$$
,
$$d = 1$$
,
$$c = 0$$
then
False

Let's take the limit
we find
False
The rate of convergence of the power series
The answer [src] 
1550995528383
-------------
1250000000000
$$\frac{1550995528383}{1250000000000}$$ 
1550995528383/1250000000000
Numerical answer
The series diverges
The graph
Sum of series (n-1)*((6!)/((n!)*((6-n)!)))*(0,21^n*n!)/(1!*1^(6-n))*(0,174)

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