Mister Exam

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Sum of series:
(1+(-3)^n)/6^n
1/((2n-1)(2n+5))
sin(pi*sqrt(n^2+k^2))
ln(n/10)/(exp(n/10)+1)
Identical expressions
(one +(- three)^n)/ six ^n
(1 plus ( minus 3) to the power of n) divide by 6 to the power of n
(one plus ( minus three) to the power of n) divide by six to the power of n
(1+(-3)n)/6n
1+-3n/6n
1+-3^n/6^n
(1+(-3)^n) divide by 6^n
Similar expressions
(1-(-3)^n)/6^n
(1+(3)^n)/6^n

Sum of series/ (1+(-3)^n)/6^n

Sum of series (1+(-3)^n)/6^n

The solution

You have entered [src]

  oo           
____           
\   `          
 \            n
  \   1 + (-3) 
   )  ---------
  /        n   
 /        6    
/___,          
n = 0

$$\sum_{n=0}^{\infty} \frac{\left(-3\right)^{n} + 1}{6^{n}}$$

Sum((1 + (-3)^n)/6^n, (n, 0, oo))

The rate of convergence of the power series

The answer [src]

28
--
15

$$\frac{28}{15}$$

28/15

Numerical answer [src]

1.86666666666666666666666666667

1.86666666666666666666666666667

The graph

Sum of series (1+(-3)^n)/6^n

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
```