Mister Exam

Other calculators

  • How to use it?

  • Sum of series:
  • x^n/n
  • n^2*x^(n-1)
  • 1/n^1,5 1/n^1,5
  • 14/49n^2-14n-48 14/49n^2-14n-48

  • Identical expressions

  • n*i/ two ^(i+ one)
  • n multiply by i divide by 2 to the power of (i plus 1)
  • n multiply by i divide by two to the power of (i plus one)
  • n*i/2(i+1)
  • n*i/2i+1
  • ni/2^(i+1)
  • ni/2(i+1)
  • ni/2i+1
  • ni/2^i+1
  • n*i divide by 2^(i+1)

  • Similar expressions

  • n*i/2^(i-1)
Sum of series/ n*i/2^(i+1)

Sum of series n*i/2^(i+1)


∑
=

The solution

You have entered [src] 
  oo        
____        
\   `       
 \     n*I  
  \   ------
  /    I + 1
 /    2     
/___,       
n = 0
∑n=0∞in21+i\sum_{n=0}^{\infty} \frac{i n}{2^{1 + i}} 
Sum((n*i)/2^(i + 1), (n, 0, oo))
The radius of convergence of the power series
Given number:
in21+i\frac{i n}{2^{1 + i}}
It is a series of species
an(cx−x0)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+lim⁡n→∞∣anan+1∣cR^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}
In this case
an=2−1−iina_{n} = 2^{-1 - i} i n
and
x0=0x_{0} = 0
,
d=0d = 0
,
c=1c = 1
then
1=lim⁡n→∞(nn+1)1 = \lim_{n \to \infty}\left(\frac{n}{n + 1}\right)
Let's take the limit
we find
True

False
The answer [src] 
      -I
oo*I*2
∞2−ii\infty 2^{- i} i 
oo*i*2^(-i)
Numerical answer
The series diverges

    Examples of finding the sum of a series

    © Mister Exam – Calculator