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Sum of series:
x^n/2^n
ln(1+1/n)
log((-1)^n/3^n)
15
Identical expressions
log((- one)^n/ three ^n)
logarithm of (( minus 1) to the power of n divide by 3 to the power of n)
logarithm of (( minus one) to the power of n divide by three to the power of n)
log((-1)n/3n)
log-1n/3n
log-1^n/3^n
log((-1)^n divide by 3^n)
Similar expressions
log((1)^n/3^n)

Sum of series log((-1)^n/3^n)

The solution

You have entered [src]

  oo            
____            
\   `           
 \       /    n\
  \      |(-1) |
   )  log|-----|
  /      |   n |
 /       \  3  /
/___,           
n = 1

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

Sum(log((-1)^n/3^n), (n, 1, oo))

The answer [src]

  oo                
 ___                
 \  `               
  \      /    n  -n\
  /   log\(-1) *3  /
 /__,               
n = 1

$$\sum_{n=1}^{\infty} \log{\left(\left(-1\right)^{n} 3^{- n} \right)}$$

Sum(log((-1)^n*3^(-n)), (n, 1, oo))

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 log((-1)^n/3^n)

The solution

Examples of finding the sum of a series