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Sum of series:
(-1/2)^n
1/(3n+1)(3n+4)
e^(-n)
1/((5n-4)(5n+1))
Identical expressions
cos(k)/ two ^k
co sinus of e of (k) divide by 2 to the power of k
co sinus of e of (k) divide by two to the power of k
cos(k)/2k
cosk/2k
cosk/2^k
cos(k) divide by 2^k

Sum of series/ cos(k)/2^k

Sum of series cos(k)/2^k

The solution

You have entered [src]

  n         
____        
\   `       
 \    cos(k)
  \   ------
  /      k  
 /      2   
/___,       
k = 1

$$\sum_{k=1}^{n} \frac{\cos{\left(k \right)}}{2^{k}}$$

Sum(cos(k)/2^k, (k, 1, n))

The rate of convergence of the power series

The answer [src]

  n             
 ___            
 \  `           
  \    -k       
  /   2  *cos(k)
 /__,           
k = 1

$$\sum_{k=1}^{n} 2^{- k} \cos{\left(k \right)}$$

Sum(2^(-k)*cos(k), (k, 1, n))

The graph

Sum of series cos(k)/2^k

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
```