Mister Exam

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Sum of series 1/(3n+1)(3n+4)

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  oo         
 ___         
 \  `        
  \   3*n + 4
   )  -------
  /   3*n + 1
 /__,        
n = 1

\sum_{n=1}^{\infty} \frac{3 n + 4}{3 n + 1}

Sum((3*n + 4)/(3*n + 1), (n, 1, oo))

The radius of convergence of the power series

Given number:

\frac{3 n + 4}{3 n + 1}

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{3 n + 4}{3 n + 1}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty}\left(\frac{\left(3 n + 4\right)^{2}}{\left(3 n + 1\right) \left(3 n + 7\right)}\right)

True

False

The rate of convergence of the power series

The answer [src]

oo

\infty

oo

Numerical answer

The series diverges

The graph

Sum of series 1/(3*n+1)(3*n+4)