Mister Exam

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Sum of series:
x^n/sqrt(n+1)
x^2j
3/n
1-cos(pi/n)
Identical expressions
(n- one)/ two ^(n- one)
(n minus 1) divide by 2 to the power of (n minus 1)
(n minus one) divide by two to the power of (n minus one)
(n-1)/2(n-1)
n-1/2n-1
n-1/2^n-1
(n-1) divide by 2^(n-1)
Similar expressions
(n+1)/2^(n-1)
(n-1)/2^(n+1)

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

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

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)

Examples of finding the sum of a series

The Sum of the Power Series
```
x^n/n
```
```
(x-1)^n
```
Factorial
```
1/2^(n!)
```
```
n^2/n!
```
```
x^n/n!
```
```
k!/(n!*(n+k)!)
```
Flint Hills Series
```
csc(n)^2/n^3
```
Basel problem
```
1/n^2
```
```
1/n^4
```
```
1/n^6
```
Harmonic series
```
1/n
```
Grandi's series
```
(-1)^n
```
Alternating series
```
(-1)^(n + 1)/n
```
```
(n + 2)*(-1)^(n - 1)
```
```
(3*n - 1)/(-5)^n
```
```
(-1)^(n - 1)*n/(6*n - 5)
```
Newton–Mercator series
```
(-1)^(n + 1)/n*x^n
```
Exam the series for convergence
```
(3*n - 1)/(-5)^n
```