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2.87+sqrt(1+0.242*(i+0.5))
Suma de la serie/ 2.87+sqrt(1+0.242*(i+0.5))

Suma de la serie 2.87+sqrt(1+0.242*(i+0.5))


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Solución

Ha introducido [src] 
  32                                 
____                                 
\   `                                
 \    /          ___________________\
  \   |287      /     121*(i + 1/2) |
  /   |--- +   /  1 + ------------- |
 /    \100   \/            500      /
/___,                                
i = 1
$$\sum_{i=1}^{32} \left(\sqrt{\frac{121 \left(i + \frac{1}{2}\right)}{500} + 1} + \frac{287}{100}\right)$$ 
Sum(287/100 + sqrt(1 + 121*(i + 1/2)/500), (i, 1, 32))
Velocidad de la convergencia de la serie
Respuesta [src] 
         _____     ______     ______     ______     ______     ______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______     _______       _____       ______       ______       ______        _____        _____
2296   \/ 642    \/ 1126    \/ 1610    \/ 2094    \/ 2578    \/ 3062    \/ 13630    \/ 18470    \/ 20890    \/ 25730    \/ 30570    \/ 32990    \/ 35410    \/ 37830    \/ 42670    \/ 47510    \/ 49930    \/ 54770    \/ 57190    \/ 59610    \/ 62030    \/ 71710    \/ 74130    \/ 78970    \/ 81390    \/ 86230    3*\/ 394    3*\/ 2590    3*\/ 5010    3*\/ 7430    13*\/ 410    17*\/ 290 
---- + ------- + -------- + -------- + -------- + -------- + -------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + ---------- + ---------- + ---------- + ---------- + ----------
 25       20        20         20         20         20         20         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100         100          20         100          100          100          100          100
$$\frac{\sqrt{13630}}{100} + \frac{\sqrt{642}}{20} + \frac{\sqrt{18470}}{100} + \frac{\sqrt{20890}}{100} + \frac{3 \sqrt{2590}}{100} + \frac{\sqrt{25730}}{100} + \frac{\sqrt{1126}}{20} + \frac{\sqrt{30570}}{100} + \frac{\sqrt{32990}}{100} + \frac{\sqrt{35410}}{100} + \frac{\sqrt{37830}}{100} + \frac{\sqrt{1610}}{20} + \frac{\sqrt{42670}}{100} + \frac{3 \sqrt{5010}}{100} + \frac{\sqrt{47510}}{100} + \frac{\sqrt{49930}}{100} + \frac{\sqrt{2094}}{20} + \frac{\sqrt{54770}}{100} + \frac{\sqrt{57190}}{100} + \frac{\sqrt{59610}}{100} + \frac{\sqrt{62030}}{100} + \frac{\sqrt{2578}}{20} + \frac{3 \sqrt{7430}}{100} + \frac{13 \sqrt{410}}{100} + \frac{\sqrt{71710}}{100} + \frac{\sqrt{74130}}{100} + \frac{\sqrt{3062}}{20} + \frac{\sqrt{78970}}{100} + \frac{\sqrt{81390}}{100} + \frac{17 \sqrt{290}}{100} + \frac{\sqrt{86230}}{100} + \frac{3 \sqrt{394}}{20} + \frac{2296}{25}$$ 
2296/25 + sqrt(642)/20 + sqrt(1126)/20 + sqrt(1610)/20 + sqrt(2094)/20 + sqrt(2578)/20 + sqrt(3062)/20 + sqrt(13630)/100 + sqrt(18470)/100 + sqrt(20890)/100 + sqrt(25730)/100 + sqrt(30570)/100 + sqrt(32990)/100 + sqrt(35410)/100 + sqrt(37830)/100 + sqrt(42670)/100 + sqrt(47510)/100 + sqrt(49930)/100 + sqrt(54770)/100 + sqrt(57190)/100 + sqrt(59610)/100 + sqrt(62030)/100 + sqrt(71710)/100 + sqrt(74130)/100 + sqrt(78970)/100 + sqrt(81390)/100 + sqrt(86230)/100 + 3*sqrt(394)/20 + 3*sqrt(2590)/100 + 3*sqrt(5010)/100 + 3*sqrt(7430)/100 + 13*sqrt(410)/100 + 17*sqrt(290)/100
Respuesta numérica [src] 
162.236438724191713547625526230
162.236438724191713547625526230
Gráfico
Suma de la serie 2.87+sqrt(1+0.242*(i+0.5))

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