Sum of series cos(n)

The solution

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  36        
 __         
 \ `        
  )   cos(n)
 /_,        
n = 1

$$\sum_{n=1}^{36} \cos{\left(n \right)}$$

Sum(cos(n), (n, 1, 36))

The rate of convergence of the power series

The answer [src]

cos(1) + cos(2) + cos(3) + cos(4) + cos(5) + cos(6) + cos(7) + cos(8) + cos(9) + cos(10) + cos(11) + cos(12) + cos(13) + cos(14) + cos(15) + cos(16) + cos(17) + cos(18) + cos(19) + cos(20) + cos(21) + cos(22) + cos(23) + cos(24) + cos(25) + cos(26) + cos(27) + cos(28) + cos(29) + cos(30) + cos(31) + cos(32) + cos(33) + cos(34) + cos(35) + cos(36)

$$\cos{\left(22 \right)} + \cos{\left(3 \right)} + \cos{\left(28 \right)} + \cos{\left(16 \right)} + \cos{\left(9 \right)} + \cos{\left(35 \right)} + \cos{\left(34 \right)} + \cos{\left(10 \right)} + \cos{\left(15 \right)} + \cos{\left(29 \right)} + \cos{\left(4 \right)} + \cos{\left(21 \right)} + \cos{\left(23 \right)} + \cos{\left(2 \right)} + \cos{\left(27 \right)} + \cos{\left(17 \right)} + \cos{\left(8 \right)} + \cos{\left(36 \right)} + \cos{\left(33 \right)} + \cos{\left(11 \right)} + \cos{\left(14 \right)} + \cos{\left(30 \right)} + \cos{\left(5 \right)} + \cos{\left(20 \right)} + \cos{\left(24 \right)} + \cos{\left(1 \right)} + \cos{\left(26 \right)} + \cos{\left(18 \right)} + \cos{\left(7 \right)} + \cos{\left(32 \right)} + \cos{\left(12 \right)} + \cos{\left(13 \right)} + \cos{\left(31 \right)} + \cos{\left(6 \right)} + \cos{\left(19 \right)} + \cos{\left(25 \right)}$$

cos(1) + cos(2) + cos(3) + cos(4) + cos(5) + cos(6) + cos(7) + cos(8) + cos(9) + cos(10) + cos(11) + cos(12) + cos(13) + cos(14) + cos(15) + cos(16) + cos(17) + cos(18) + cos(19) + cos(20) + cos(21) + cos(22) + cos(23) + cos(24) + cos(25) + cos(26) + cos(27) + cos(28) + cos(29) + cos(30) + cos(31) + cos(32) + cos(33) + cos(34) + cos(35) + cos(36)

Numerical answer [src]

-1.47170135175454067845608770540

-1.47170135175454067845608770540

The graph

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
```

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Identical expressions

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Sum of series cos(n)

The solution

Examples of finding the sum of a series