Sr Examen

Otras calculadoras

Suma de la serie (x-3)^(n+1)/(n+1)4^(n+1)



=

Solución

Ha introducido [src]
  oo                     
____                     
\   `                    
 \           n + 1       
  \   (x - 3)       n + 1
  /   ------------*4     
 /       n + 1           
/___,                    
n = 0                    
$$\sum_{n=0}^{\infty} 4^{n + 1} \frac{\left(x - 3\right)^{n + 1}}{n + 1}$$
Sum(((x - 3)^(n + 1)/(n + 1))*4^(n + 1), (n, 0, oo))
Respuesta [src]
     // -log(13 - 4*x)                                 \       // -log(13 - 4*x)                                 \
     || ---------------    for And(x >= 11/4, x < 13/4)|       || ---------------    for And(x >= 11/4, x < 13/4)|
     ||    4*(-3 + x)                                  |       ||    4*(-3 + x)                                  |
     ||                                                |       ||                                                |
     ||  oo                                            |       ||  oo                                            |
     ||____                                            |       ||____                                            |
- 12*|<\   `                                           | + 4*x*|<\   `                                           |
     || \     n         n                              |       || \     n         n                              |
     ||  \   4 *(-3 + x)                               |       ||  \   4 *(-3 + x)                               |
     ||  /   ------------           otherwise          |       ||  /   ------------           otherwise          |
     || /       1 + n                                  |       || /       1 + n                                  |
     ||/___,                                           |       ||/___,                                           |
     \\n = 0                                           /       \\n = 0                                           /
$$4 x \left(\begin{cases} - \frac{\log{\left(13 - 4 x \right)}}{4 \left(x - 3\right)} & \text{for}\: x \geq \frac{11}{4} \wedge x < \frac{13}{4} \\\sum_{n=0}^{\infty} \frac{4^{n} \left(x - 3\right)^{n}}{n + 1} & \text{otherwise} \end{cases}\right) - 12 \left(\begin{cases} - \frac{\log{\left(13 - 4 x \right)}}{4 \left(x - 3\right)} & \text{for}\: x \geq \frac{11}{4} \wedge x < \frac{13}{4} \\\sum_{n=0}^{\infty} \frac{4^{n} \left(x - 3\right)^{n}}{n + 1} & \text{otherwise} \end{cases}\right)$$
-12*Piecewise((-log(13 - 4*x)/(4*(-3 + x)), (x >= 11/4)∧(x < 13/4)), (Sum(4^n*(-3 + x)^n/(1 + n), (n, 0, oo)), True)) + 4*x*Piecewise((-log(13 - 4*x)/(4*(-3 + x)), (x >= 11/4)∧(x < 13/4)), (Sum(4^n*(-3 + x)^n/(1 + n), (n, 0, oo)), True))

    Ejemplos de hallazgo de la suma de la serie