Mister Exam

Other calculators

2-3(0.8)^n

  • How to use it?

  • Sum of series:
  • 1/n^2 1/n^2
  • 2-3(0.8)^n 2-3(0.8)^n
  • sen((npi)/2) sen((npi)/2)
  • x*y*z

  • Identical expressions

  • two - three (zero . eight)^n
  • 2 minus 3(0.8) to the power of n
  • two minus three (zero . eight) to the power of n
  • 2-3(0.8)n
  • 2-30.8n
  • 2-30.8^n

  • Similar expressions

  • 2+3(0.8)^n
Sum of series/ 2-3(0.8)^n

Sum of series 2-3(0.8)^n


∑
=

The solution

You have entered [src] 
  oo              
 ___              
 \  `             
  \   /         n\
  /   \2 - 3*4/5 /
 /__,             
n = 1
$$\sum_{n=1}^{\infty} \left(2 - 3 \left(\frac{4}{5}\right)^{n}\right)$$ 
Sum(2 - 3*(4/5)^n, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$2 - 3 \left(\frac{4}{5}\right)^{n}$$
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
$$a_{n} = 2 - 3 \left(\frac{4}{5}\right)^{n}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} \left|{\frac{3 \left(\frac{4}{5}\right)^{n} - 2}{3 \left(\frac{4}{5}\right)^{n + 1} - 2}}\right|$$
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 2-3(0.8)^n

    Examples of finding the sum of a series

    © Mister Exam – Calculator