Mister Exam

Other calculators

1/1/(3n+2)(3n+1)

  • How to use it?

  • Sum of series:
  • a^n
  • y-xy
  • sin(1/n)n sin(1/n)n
  • k^2-3*k

  • Identical expressions

  • one / one /(3n+ two)(3n+ one)
  • 1 divide by 1 divide by (3n plus 2)(3n plus 1)
  • one divide by one divide by (3n plus two)(3n plus one)
  • 1/1/3n+23n+1
  • 1 divide by 1 divide by (3n+2)(3n+1)

  • Similar expressions

  • 1/1/(3n-2)(3n+1)
  • 1/1/(3n+2)(3n-1)
Sum of series/ 1/1/(3n+2)(3n+1)

Sum of series 1/1/(3n+2)(3n+1)


∑
=

The solution

You have entered [src] 
  oo         
 ___         
 \  `        
  \   3*n + 1
   )  -------
  /   3*n + 2
 /__,        
n = 1
$$\sum_{n=1}^{\infty} \frac{3 n + 1}{3 n + 2}$$ 
Sum((3*n + 1)/(3*n + 2), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{3 n + 1}{3 n + 2}$$
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
$$a_{n} = \frac{3 n + 1}{3 n + 2}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\left(3 n + 1\right) \left(3 n + 5\right)}{\left(3 n + 2\right) \left(3 n + 4\right)}\right)$$
Let's take the limit
we find
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 1/1/(3n+2)(3n+1)

    Examples of finding the sum of a series

    © Mister Exam – Calculator