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(n-1)/2^(n-1)

Sum of series (n-1)/2^(n-1)



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The solution

You have entered [src]
  k         
____        
\   `       
 \    n - 1 
  \   ------
  /    n - 1
 /    2     
/___,       
n = 2       
$$\sum_{n=2}^{k} \frac{n - 1}{2^{n - 1}}$$
Sum((n - 1)/2^(n - 1), (n, 2, k))
The rate of convergence of the power series
The answer [src]
        -1 - k    -k /       k      \
-1 + 4*2       - 2  *\4 - 3*2  + 2*k/
$$4 \cdot 2^{- k - 1} - 1 - 2^{- k} \left(- 3 \cdot 2^{k} + 2 k + 4\right)$$
-1 + 4*2^(-1 - k) - 2^(-k)*(4 - 3*2^k + 2*k)
The graph
Sum of series (n-1)/2^(n-1)

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