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



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Solución

Ha introducido [src]
  oo                  
____                  
\   `                 
 \         n / n    \ 
  \    (-1) *\x  + 1/ 
  /   ----------------
 /    (n + 1)*(2 + n)!
/___,                 
n = 0                 
$$\sum_{n=0}^{\infty} \frac{\left(-1\right)^{n} \left(x^{n} + 1\right)}{\left(n + 1\right) \left(n + 2\right)!}$$
Sum(((-1)^n*(x^n + 1))/(((n + 1)*factorial(2 + n))), (n, 0, oo))
Respuesta [src]
                                                   -x          /   pi*I\       /   pi*I\             
    / pi*I\    -1          EulerGamma   2 - 2*x   e     - 2*log\x*e    / + 2*Ei\x*e    /             
- Ei\e    / - e   + pi*I + ---------- + ------- - --- - -------------------------------- + EulerGamma
                               x             2      2                 2*x                            
                                          2*x      x                                                 
$$- \frac{1}{e} + \gamma - \operatorname{Ei}{\left(e^{i \pi} \right)} + i \pi - \frac{- 2 \log{\left(x e^{i \pi} \right)} + 2 \operatorname{Ei}{\left(x e^{i \pi} \right)}}{2 x} + \frac{\gamma}{x} + \frac{2 - 2 x}{2 x^{2}} - \frac{e^{- x}}{x^{2}}$$
-Ei(exp_polar(pi*i)) - exp(-1) + pi*i + EulerGamma/x + (2 - 2*x)/(2*x^2) - exp(-x)/x^2 - (-2*log(x*exp_polar(pi*i)) + 2*Ei(x*exp_polar(pi*i)))/(2*x) + EulerGamma

    Ejemplos de hallazgo de la suma de la serie