Mister Exam

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Sum of series:
x*1,2^n
(4i+5)/10^2
x1
n/2^n*z^2n
Identical expressions
x* one , two ^n
x multiply by 1,2 to the power of n
x multiply by one , two to the power of n
x*1,2n
x1,2^n
x1,2n

Sum of series/ x*1,2^n

Sum of series x*1,2^n

The solution

You have entered [src]

  20        
 ___        
 \  `       
  \        n
  /   x*6/5 
 /__,       
n = 0

$$\sum_{n=0}^{20} \left(\frac{6}{5}\right)^{n} x$$

Sum(x*(6/5)^n, (n, 0, 20))

The answer [src]

21460113482174731*x
-------------------
   95367431640625

$$\frac{21460113482174731 x}{95367431640625}$$

21460113482174731*x/95367431640625

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
```