Mister Exam

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Sum of series:
1/(n*ln^2n)
(3*n/(9*n-1))^n
sin(pi/n)^n
((-1)^n)(pi^(2n))/((6^(2n))(2n)!)
Identical expressions
(three *n/(nine *n- one))^n
(3 multiply by n divide by (9 multiply by n minus 1)) to the power of n
(three multiply by n divide by (nine multiply by n minus one)) to the power of n
(3*n/(9*n-1))n
3*n/9*n-1n
(3n/(9n-1))^n
(3n/(9n-1))n
3n/9n-1n
3n/9n-1^n
(3*n divide by (9*n-1))^n
Similar expressions
(3*n/(9*n+1))^n

Sum of series/ (3*n/(9*n-1))^n

Sum of series (3n/(9n-1))^n

You have entered [src]

  oo            
____            
\   `           
 \             n
  \   /  3*n  \ 
  /   |-------| 
 /    \9*n - 1/ 
/___,           
n = 1

\sum_{n=1}^{\infty} \left(\frac{3 n}{9 n - 1}\right)^{n}

Sum(((3*n)/(9*n - 1))^n, (n, 1, oo))

The radius of convergence of the power series

Given number:

\left(\frac{3 n}{9 n - 1}\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{3 n}{9 n - 1}\right)^{n}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty}\left(\left(\frac{3 \left(n + 1\right)}{9 n + 8}\right)^{- n - 1} \left|{\left(\frac{3 n}{9 n - 1}\right)^{n}}\right|\right)

False

False

The rate of convergence of the power series

The answer [src]

  oo             
____             
\   `            
 \              n
  \   /  3*n   \ 
  /   |--------| 
 /    \-1 + 9*n/ 
/___,            
n = 1

\sum_{n=1}^{\infty} \left(\frac{3 n}{9 n - 1}\right)^{n}

Sum((3*n/(-1 + 9*n))^n, (n, 1, oo))

Numerical answer [src]

0.561769005363273344436983043632

0.561769005363273344436983043632

The graph

Sum of series (3*n/(9*n-1))^n