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sin(4^k)/(2^(2*k)*(2*k)!)
Suma de la serie/ sin(4^k)/(2^(2*k)*(2*k)!)

Suma de la serie sin(4^k)/(2^(2*k)*(2*k)!)


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Solución

Ha introducido [src] 
  6              
____             
\   `            
 \         / k\  
  \     sin\4 /  
   )  -----------
  /    2*k       
 /    2   *(2*k)!
/___,            
k = 1
$$\sum_{k=1}^{6} \frac{\sin{\left(4^{k} \right)}}{2^{2 k} \left(2 k\right)!}$$ 
Sum(sin(4^k)/((2^(2*k)*factorial(2*k))), (k, 1, 6))
Velocidad de la convergencia de la serie
Respuesta [src] 
sin(4)   sin(16)   sin(64)   sin(256)   sin(1024)      sin(4096)  
------ + ------- + ------- + -------- + ---------- + -------------
  8        384      46080    10321920   3715891200   1961990553600
$$\frac{\sin{\left(4 \right)}}{8} + \frac{\sin{\left(16 \right)}}{384} + \frac{\sin{\left(256 \right)}}{10321920} + \frac{\sin{\left(1024 \right)}}{3715891200} + \frac{\sin{\left(4096 \right)}}{1961990553600} + \frac{\sin{\left(64 \right)}}{46080}$$ 
sin(4)/8 + sin(16)/384 + sin(64)/46080 + sin(256)/10321920 + sin(1024)/3715891200 + sin(4096)/1961990553600
Respuesta numérica [src] 
-0.0953301911385706540747011626420
-0.0953301911385706540747011626420
Gráfico
Suma de la serie sin(4^k)/(2^(2*k)*(2*k)!)

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