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Sum of series:
n^2*x^n
9/(9n^2+21n-8)
(n^3+n+5)/(n+6)
sen(ix)
Identical expressions
one +(two (- one)^(n+ one))/(k^ two - one)coskx
1 plus (2( minus 1) to the power of (n plus 1)) divide by (k squared minus 1) co sinus of e of kx
one plus (two ( minus one) to the power of (n plus one)) divide by (k to the power of two minus one) co sinus of e of kx
1+(2(-1)(n+1))/(k2-1)coskx
1+2-1n+1/k2-1coskx
1+(2(-1)^(n+1))/(k²-1)coskx
1+(2(-1) to the power of (n+1))/(k to the power of 2-1)coskx
1+2-1^n+1/k^2-1coskx
1+(2(-1)^(n+1)) divide by (k^2-1)coskx
Similar expressions
1+(2(-1)^(n+1))/(k^2+1)coskx
1-(2(-1)^(n+1))/(k^2-1)coskx
1+(2(1)^(n+1))/(k^2-1)coskx
1+(2(-1)^(n-1))/(k^2-1)coskx

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

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

The solution

You have entered [src]

  oo                            
____                            
\   `                           
 \    /          n + 1         \
  \   |    2*(-1)              |
   )  |1 + -----------*cos(k*x)|
  /   |        2               |
 /    \       k  - 1           /
/___,                           
n = 1

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

Sum(1 + ((2*(-1)^(n + 1))/(k^2 - 1))*cos(k*x), (n, 1, oo))

The answer [src]

  oo                            
____                            
\   `                           
 \    /          1 + n         \
  \   |    2*(-1)     *cos(k*x)|
   )  |1 + --------------------|
  /   |                2       |
 /    \          -1 + k        /
/___,                           
n = 1

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

Sum(1 + 2*(-1)^(1 + n)*cos(k*x)/(-1 + k^2), (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 1+(2(-1)^(n+1))/(k^2-1)coskx

The solution

Examples of finding the sum of a series