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5*sin(sqrt(i*0.2))/25

Suma de la serie 5*sin(sqrt(i*0.2))/25



=

Solución

Ha introducido [src]
  25                 
_____                
\    `               
 \          /    ___\
  \         |   / i |
   \   5*sin|  /  - |
   /        \\/   5 /
  /    --------------
 /           25      
/____,               
i = 1                
$$\sum_{i=1}^{25} \frac{5 \sin{\left(\sqrt{\frac{i}{5}} \right)}}{25}$$
Sum((5*sin(sqrt(i/5)))/25, (i, 1, 25))
Velocidad de la convergencia de la serie
Respuesta [src]
                                                            /  ___\      /  ____\      /  ____\      /  ____\      /  ____\      /  ____\      /  ____\      /  ____\      /  ____\      /  ____\      /  _____\      /  _____\      /  _____\      /    ___\      /    ____\      /    ____\      /    ____\      /    ___\      /    ____\      /    ___\
                                                            |\/ 5 |      |\/ 10 |      |\/ 15 |      |\/ 30 |      |\/ 35 |      |\/ 55 |      |\/ 65 |      |\/ 70 |      |\/ 85 |      |\/ 95 |      |\/ 105 |      |\/ 110 |      |\/ 115 |      |2*\/ 5 |      |2*\/ 10 |      |2*\/ 15 |      |2*\/ 30 |      |3*\/ 5 |      |3*\/ 10 |      |4*\/ 5 |
                     /  ___\      /  ___\      /  ___\   sin|-----|   sin|------|   sin|------|   sin|------|   sin|------|   sin|------|   sin|------|   sin|------|   sin|------|   sin|------|   sin|-------|   sin|-------|   sin|-------|   sin|-------|   sin|--------|   sin|--------|   sin|--------|   sin|-------|   sin|--------|   sin|-------|
sin(1)   sin(2)   sin\\/ 2 /   sin\\/ 3 /   sin\\/ 5 /      \  5  /      \  5   /      \  5   /      \  5   /      \  5   /      \  5   /      \  5   /      \  5   /      \  5   /      \  5   /      \   5   /      \   5   /      \   5   /      \   5   /      \   5    /      \   5    /      \   5    /      \   5   /      \   5    /      \   5   /
------ + ------ + ---------- + ---------- + ---------- + ---------- + ----------- + ----------- + ----------- + ----------- + ----------- + ----------- + ----------- + ----------- + ----------- + ------------ + ------------ + ------------ + ------------ + ------------- + ------------- + ------------- + ------------ + ------------- + ------------
  5        5          5            5            5            5             5             5             5             5             5             5             5             5             5             5              5              5              5               5               5               5              5               5              5      
$$\frac{\sin{\left(\frac{\sqrt{5}}{5} \right)}}{5} + \frac{\sin{\left(\frac{\sqrt{10}}{5} \right)}}{5} + \frac{\sin{\left(\frac{\sqrt{15}}{5} \right)}}{5} + \frac{\sin{\left(\frac{2 \sqrt{5}}{5} \right)}}{5} + \frac{\sin{\left(\sqrt{5} \right)}}{5} + \frac{\sin{\left(\frac{2 \sqrt{30}}{5} \right)}}{5} + \frac{\sin{\left(\frac{\sqrt{115}}{5} \right)}}{5} + \frac{\sin{\left(1 \right)}}{5} + \frac{\sin{\left(\frac{\sqrt{110}}{5} \right)}}{5} + \frac{\sin{\left(\frac{\sqrt{105}}{5} \right)}}{5} + \frac{\sin{\left(\frac{\sqrt{30}}{5} \right)}}{5} + \frac{\sin{\left(2 \right)}}{5} + \frac{\sin{\left(\frac{\sqrt{35}}{5} \right)}}{5} + \frac{\sin{\left(\frac{\sqrt{95}}{5} \right)}}{5} + \frac{\sin{\left(\frac{3 \sqrt{10}}{5} \right)}}{5} + \frac{\sin{\left(\frac{2 \sqrt{10}}{5} \right)}}{5} + \frac{\sin{\left(\frac{\sqrt{85}}{5} \right)}}{5} + \frac{\sin{\left(\frac{3 \sqrt{5}}{5} \right)}}{5} + \frac{\sin{\left(\frac{4 \sqrt{5}}{5} \right)}}{5} + \frac{\sin{\left(\sqrt{3} \right)}}{5} + \frac{\sin{\left(\sqrt{2} \right)}}{5} + \frac{\sin{\left(\frac{\sqrt{70}}{5} \right)}}{5} + \frac{\sin{\left(\frac{\sqrt{55}}{5} \right)}}{5} + \frac{\sin{\left(\frac{\sqrt{65}}{5} \right)}}{5} + \frac{\sin{\left(\frac{2 \sqrt{15}}{5} \right)}}{5}$$
sin(1)/5 + sin(2)/5 + sin(sqrt(2))/5 + sin(sqrt(3))/5 + sin(sqrt(5))/5 + sin(sqrt(5)/5)/5 + sin(sqrt(10)/5)/5 + sin(sqrt(15)/5)/5 + sin(sqrt(30)/5)/5 + sin(sqrt(35)/5)/5 + sin(sqrt(55)/5)/5 + sin(sqrt(65)/5)/5 + sin(sqrt(70)/5)/5 + sin(sqrt(85)/5)/5 + sin(sqrt(95)/5)/5 + sin(sqrt(105)/5)/5 + sin(sqrt(110)/5)/5 + sin(sqrt(115)/5)/5 + sin(2*sqrt(5)/5)/5 + sin(2*sqrt(10)/5)/5 + sin(2*sqrt(15)/5)/5 + sin(2*sqrt(30)/5)/5 + sin(3*sqrt(5)/5)/5 + sin(3*sqrt(10)/5)/5 + sin(4*sqrt(5)/5)/5
Respuesta numérica [src]
4.39372360697007672687733199927
4.39372360697007672687733199927
Gráfico
Suma de la serie 5*sin(sqrt(i*0.2))/25

    Ejemplos de hallazgo de la suma de la serie