Mister Exam

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Sum of series:
n^2/3^n
1/((3*n+1)*(3*n+4))
sin(n*x)/n^2
sin²n/√n³+5
Identical expressions
cos(five *x)*sin(two *x)
co sinus of e of (5 multiply by x) multiply by sinus of (2 multiply by x)
co sinus of e of (five multiply by x) multiply by sinus of (two multiply by x)
cos(5x)sin(2x)
cos5xsin2x

Sum of series/ cos(5*x)*sin(2*x)

Sum of series cos(5x)sin(2*x)

The solution

You have entered [src]

  15                   
 __                    
 \ `                   
  )   cos(5*x)*sin(2*x)
 /_,                   
n = 1

$$\sum_{n=1}^{15} \sin{\left(2 x \right)} \cos{\left(5 x \right)}$$

Sum(cos(5*x)*sin(2*x), (n, 1, 15))

The answer [src]

15*cos(5*x)*sin(2*x)

$$15 \sin{\left(2 x \right)} \cos{\left(5 x \right)}$$

15*cos(5*x)*sin(2*x)

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
```