Mister Exam

Other calculators


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

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



=

The solution

You have entered [src]
  oo         
 ___         
 \  `        
  \   3*n + 1
   )  -------
  /   3*n + 2
 /__,        
n = 1        
n=13n+13n+2\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:
3n+13n+2\frac{3 n + 1}{3 n + 2}
It is a series of species
an(cxx0)dna_{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:
Rd=x0+limnanan+1cR^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}
In this case
an=3n+13n+2a_{n} = \frac{3 n + 1}{3 n + 2}
and
x0=0x_{0} = 0
,
d=0d = 0
,
c=1c = 1
then
1=limn((3n+1)(3n+5)(3n+2)(3n+4))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
1.07.01.52.02.53.03.54.04.55.05.56.06.5010
The answer [src]
oo
\infty
oo
Numerical answer
The series diverges
The graph
Sum of series 1/(3n+2)(3n+1)

    Examples of finding the sum of a series