Sr Examen

Otras calculadoras

Suma de la serie ((-1)^(n+1)x^(2n-1))/(2n-1)



=

Solución

Ha introducido [src]
  oo                    
____                    
\   `                   
 \        n + 1  2*n - 1
  \   (-1)     *x       
  /   ------------------
 /         2*n - 1      
/___,                   
n = 1                   
$$\sum_{n=1}^{\infty} \frac{\left(-1\right)^{n + 1} x^{2 n - 1}}{2 n - 1}$$
Sum(((-1)^(n + 1)*x^(2*n - 1))/(2*n - 1), (n, 1, oo))
Respuesta [src]
 //    -atan(x)      for And(x >= -1, x <= 1)\
 ||                                          |
 ||  oo                                      |
 ||____                                      |
 ||\   `                                     |
-|< \        n  2*n                          |
 ||  \   (-1) *x                             |
 ||  /   ----------         otherwise        |
 || /    -x + 2*n*x                          |
 ||/___,                                     |
 \\n = 1                                     /
$$- \begin{cases} - \operatorname{atan}{\left(x \right)} & \text{for}\: x \geq -1 \wedge x \leq 1 \\\sum_{n=1}^{\infty} \frac{\left(-1\right)^{n} x^{2 n}}{2 n x - x} & \text{otherwise} \end{cases}$$
-Piecewise((-atan(x), (x >= -1)∧(x <= 1)), (Sum((-1)^n*x^(2*n)/(-x + 2*n*x), (n, 1, oo)), True))

    Ejemplos de hallazgo de la suma de la serie