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Sum of series:
(2^n+(-1)^n)/5^n
1/(4n^2-1)
(n+1)/n
(3^n-2^n)/6^n
Identical expressions
(two ^n+(- one)^n)/ five ^n
(2 to the power of n plus ( minus 1) to the power of n) divide by 5 to the power of n
(two to the power of n plus ( minus one) to the power of n) divide by five to the power of n
(2n+(-1)n)/5n
2n+-1n/5n
2^n+-1^n/5^n
(2^n+(-1)^n) divide by 5^n
Similar expressions
(2^n-(-1)^n)/5^n
(2^n+(1)^n)/5^n

Sum of series/ (2^n+(-1)^n)/5^n

Sum of series (2^n+(-1)^n)/5^n

The solution

You have entered [src]

  oo            
____            
\   `           
 \     n       n
  \   2  + (-1) 
   )  ----------
  /        n    
 /        5     
/___,           
n = 1

$$\sum_{n=1}^{\infty} \frac{\left(-1\right)^{n} + 2^{n}}{5^{n}}$$

Sum((2^n + (-1)^n)/5^n, (n, 1, oo))

The rate of convergence of the power series

The answer [src]

1/2

$$\frac{1}{2}$$

1/2

Numerical answer [src]

0.500000000000000000000000000000

0.500000000000000000000000000000

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

Similar expressions

Sum of series (2^n+(-1)^n)/5^n

The solution

Examples of finding the sum of a series