Mister Exam
Other calculators
- Taylor Series Step by Step
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- Product of series
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How to use it?
- Sum of series:
- nx^n/(8n-9)*3^n
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sqrt(n+1)-sqrt(n)/sqrt(n^2+n)
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cos(i*n)/2^n
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(3*x^2-2*x+3)/factorial(x+1)
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Identical expressions
- sin(three *n)/(n+ two)
- sinus of (3 multiply by n) divide by (n plus 2)
- sinus of (three multiply by n) divide by (n plus two)
- sin(3n)/(n+2)
- sin3n/n+2
- sin(3*n) divide by (n+2)
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Similar expressions
- sin(3*n)/(n-2)
Sum of series sin(3*n)/(n+2)
The solution
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[src]
68 ___ \ ` \ sin(3*n) ) -------- / n + 2 /__, n = 1
$$\sum_{n=1}^{68} \frac{\sin{\left(3 n \right)}}{n + 2}$$
Sum(sin(3*n)/(n + 2), (n, 1, 68))
The rate of convergence of the power series
The answer
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sin(3) sin(6) sin(9) sin(12) sin(15) sin(18) sin(21) sin(24) sin(27) sin(30) sin(33) sin(36) sin(39) sin(42) sin(45) sin(48) sin(51) sin(54) sin(57) sin(60) sin(63) sin(66) sin(69) sin(72) sin(75) sin(78) sin(81) sin(84) sin(87) sin(90) sin(93) sin(96) sin(99) sin(102) sin(105) sin(108) sin(111) sin(114) sin(117) sin(120) sin(123) sin(126) sin(129) sin(132) sin(135) sin(138) sin(141) sin(144) sin(147) sin(150) sin(153) sin(156) sin(159) sin(162) sin(165) sin(168) sin(171) sin(174) sin(177) sin(180) sin(183) sin(186) sin(189) sin(192) sin(195) sin(198) sin(201) sin(204) ------ + ------ + ------ + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70
$$\frac{\sin{\left(18 \right)}}{8} + \frac{\sin{\left(24 \right)}}{10} + \frac{\sin{\left(12 \right)}}{6} + \frac{\sin{\left(30 \right)}}{12} + \frac{\sin{\left(36 \right)}}{14} + \frac{\sin{\left(6 \right)}}{4} + \frac{\sin{\left(42 \right)}}{16} + \frac{\sin{\left(48 \right)}}{18} + \frac{\sin{\left(93 \right)}}{33} + \frac{\sin{\left(99 \right)}}{35} + \frac{\sin{\left(54 \right)}}{20} + \frac{\sin{\left(87 \right)}}{31} + \frac{\sin{\left(105 \right)}}{37} + \frac{\sin{\left(111 \right)}}{39} + \frac{\sin{\left(81 \right)}}{29} + \frac{\sin{\left(162 \right)}}{56} + \frac{\sin{\left(168 \right)}}{58} + \frac{\sin{\left(117 \right)}}{41} + \frac{\sin{\left(156 \right)}}{54} + \frac{\sin{\left(174 \right)}}{60} + \frac{\sin{\left(75 \right)}}{27} + \frac{\sin{\left(60 \right)}}{22} + \frac{\sin{\left(150 \right)}}{52} + \frac{\sin{\left(180 \right)}}{62} + \frac{\sin{\left(123 \right)}}{43} + \frac{\sin{\left(144 \right)}}{50} + \frac{\sin{\left(186 \right)}}{64} + \frac{\sin{\left(192 \right)}}{66} + \frac{\sin{\left(138 \right)}}{48} + \frac{\sin{\left(69 \right)}}{25} + \frac{\sin{\left(129 \right)}}{45} + \frac{\sin{\left(198 \right)}}{68} + \frac{\sin{\left(66 \right)}}{24} + \frac{\sin{\left(201 \right)}}{69} + \frac{\sin{\left(132 \right)}}{46} + \frac{\sin{\left(135 \right)}}{47} + \frac{\sin{\left(204 \right)}}{70} + \frac{\sin{\left(195 \right)}}{67} + \frac{\sin{\left(63 \right)}}{23} + \frac{\sin{\left(141 \right)}}{49} + \frac{\sin{\left(189 \right)}}{65} + \frac{\sin{\left(126 \right)}}{44} + \frac{\sin{\left(72 \right)}}{26} + \frac{\sin{\left(183 \right)}}{63} + \frac{\sin{\left(147 \right)}}{51} + \frac{\sin{\left(120 \right)}}{42} + \frac{\sin{\left(177 \right)}}{61} + \frac{\sin{\left(153 \right)}}{53} + \frac{\sin{\left(171 \right)}}{59} + \frac{\sin{\left(159 \right)}}{55} + \frac{\sin{\left(165 \right)}}{57} + \frac{\sin{\left(78 \right)}}{28} + \frac{\sin{\left(114 \right)}}{40} + \frac{\sin{\left(57 \right)}}{21} + \frac{\sin{\left(108 \right)}}{38} + \frac{\sin{\left(84 \right)}}{30} + \frac{\sin{\left(102 \right)}}{36} + \frac{\sin{\left(90 \right)}}{32} + \frac{\sin{\left(96 \right)}}{34} + \frac{\sin{\left(51 \right)}}{19} + \frac{\sin{\left(3 \right)}}{3} + \frac{\sin{\left(45 \right)}}{17} + \frac{\sin{\left(39 \right)}}{15} + \frac{\sin{\left(33 \right)}}{13} + \frac{\sin{\left(9 \right)}}{5} + \frac{\sin{\left(27 \right)}}{11} + \frac{\sin{\left(15 \right)}}{7} + \frac{\sin{\left(21 \right)}}{9}$$
sin(3)/3 + sin(6)/4 + sin(9)/5 + sin(12)/6 + sin(15)/7 + sin(18)/8 + sin(21)/9 + sin(24)/10 + sin(27)/11 + sin(30)/12 + sin(33)/13 + sin(36)/14 + sin(39)/15 + sin(42)/16 + sin(45)/17 + sin(48)/18 + sin(51)/19 + sin(54)/20 + sin(57)/21 + sin(60)/22 + sin(63)/23 + sin(66)/24 + sin(69)/25 + sin(72)/26 + sin(75)/27 + sin(78)/28 + sin(81)/29 + sin(84)/30 + sin(87)/31 + sin(90)/32 + sin(93)/33 + sin(96)/34 + sin(99)/35 + sin(102)/36 + sin(105)/37 + sin(108)/38 + sin(111)/39 + sin(114)/40 + sin(117)/41 + sin(120)/42 + sin(123)/43 + sin(126)/44 + sin(129)/45 + sin(132)/46 + sin(135)/47 + sin(138)/48 + sin(141)/49 + sin(144)/50 + sin(147)/51 + sin(150)/52 + sin(153)/53 + sin(156)/54 + sin(159)/55 + sin(162)/56 + sin(165)/57 + sin(168)/58 + sin(171)/59 + sin(174)/60 + sin(177)/61 + sin(180)/62 + sin(183)/63 + sin(186)/64 + sin(189)/65 + sin(192)/66 + sin(195)/67 + sin(198)/68 + sin(201)/69 + sin(204)/70
The graph
Examples of finding the sum of a series
- The Sum of the Power Series
x^n/n
(x-1)^n
- Factorial
1/2^(n!)
n^2/n!
x^n/n!
k!/(n!*(n+k)!)
- Flint Hills Series
csc(n)^2/n^3
- Basel problem
1/n^2
1/n^4
1/n^6
- Harmonic series
1/n
- Grandi's series
(-1)^n
- Alternating series
(-1)^(n + 1)/n
(n + 2)*(-1)^(n - 1)
(3*n - 1)/(-5)^n
(-1)^(n - 1)*n/(6*n - 5)
- Newton–Mercator series
(-1)^(n + 1)/n*x^n
- Exam the series for convergence
(3*n - 1)/(-5)^n