Mister Exam

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Sum of series:
(4*9^n-2^n)/18^n
1/((3*n+1)*(3*n+4))
sqrt(n)*(x+3)^n/n^2+1
ln((n(n+2))/(n+1)^2)
Identical expressions
one /(cos(x)+y)
1 divide by ( co sinus of e of (x) plus y)
one divide by ( co sinus of e of (x) plus y)
1/cosx+y
1 divide by (cos(x)+y)
Similar expressions
1/(cos(x)-y)
1/(cosx+y)

Sum of series/ 1/(cos(x)+y)

Sum of series 1/(cos(x)+y)

The solution

You have entered [src]

  1             
 ___            
 \  `           
  \       1     
   )  ----------
  /   cos(x) + y
 /__,           
n = 0

$$\sum_{n=0}^{1} \frac{1}{y + \cos{\left(x \right)}}$$

Sum(1/(cos(x) + y), (n, 0, 1))

The answer [src]

    2     
----------
y + cos(x)

$$\frac{2}{y + \cos{\left(x \right)}}$$

2/(y + cos(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
```