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Sum of series:
1/n*(n+1)
7+k
6/(3n-1)(3n+5)
6/((3*n-1)*(3*n+5))
Identical expressions
(- one)^n*x^(n+ one)/factorial(n+ one)
( minus 1) to the power of n multiply by x to the power of (n plus 1) divide by factorial(n plus 1)
( minus one) to the power of n multiply by x to the power of (n plus one) divide by factorial(n plus one)
(-1)n*x(n+1)/factorial(n+1)
-1n*xn+1/factorialn+1
(-1)^nx^(n+1)/factorial(n+1)
(-1)nx(n+1)/factorial(n+1)
-1nxn+1/factorialn+1
-1^nx^n+1/factorialn+1
(-1)^n*x^(n+1) divide by factorial(n+1)
Similar expressions
(-1)^n*x^(n+1)/factorial(n-1)
(-1)^n*x^(n-1)/factorial(n+1)
(1)^n*x^(n+1)/factorial(n+1)

Sum of series/ (-1)^n*x^(n+1)/factorial(n+1)

Sum of series (-1)^n*x^(n+1)/factorial(n+1)

The solution

You have entered [src]

  oo              
____              
\   `             
 \        n  n + 1
  \   (-1) *x     
  /   ------------
 /      (n + 1)!  
/___,             
n = 0

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

Sum(((-1)^n*x^(n + 1))/factorial(n + 1), (n, 0, oo))

The answer [src]

  /     -x\
  |1   e  |
x*|- - ---|
  \x    x /

$$x \left(\frac{1}{x} - \frac{e^{- x}}{x}\right)$$

x*(1/x - exp(-x)/x)

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)^n*x^(n+1)/factorial(n+1)

The solution

Examples of finding the sum of a series