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  • Sum of series:
  • ln(n)/sqrt(n) ln(n)/sqrt(n)
  • (k^3-k^2) (k^3-k^2)
  • n*i/2^(i+1)
  • cos(n*x)/n^2

  • 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)


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The solution

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

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

    Examples of finding the sum of a series

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