Mister Exam
Other calculators
- Taylor Series Step by Step
- Fourier series step by step
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- Product of series
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How to use it?
- Sum of series:
- x^n/n
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1/n^6
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1/n^n
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(n-1)/n!
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Identical expressions
- one , ninety-nine +sqrt(one + zero . two hundred and forty-two *i)
- 1,99 plus square root of (1 plus 0.242 multiply by i)
- one , ninety minus nine plus square root of (one plus zero . two hundred and forty minus two multiply by i)
- 1,99+√(1+0.242*i)
- 1,99+sqrt(1+0.242i)
- 1,99+sqrt1+0.242i
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Similar expressions
- 1,99-sqrt(1+0.242*i)
- 1,99+sqrt(1-0.242*i)
Sum of series 1,99+sqrt(1+0.242*i)
The solution
You have entered
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32 ____ \ ` \ / ___________\ \ |199 / 121*i | / |--- + / 1 + ----- | / \100 \/ 500 / /___, i = 1
$$\sum_{i=1}^{32} \left(\sqrt{\frac{121 i}{500} + 1} + \frac{199}{100}\right)$$
Sum(199/100 + sqrt(1 + 121*i/500), (i, 1, 32))
The rate of convergence of the power series
The answer
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_____ _____ _____ _____ _____ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ _______ _______ _______ _______ _______ _______ _______ _______ _______ _______ _____ ____ _____ ______ _____ ____ 1592 \/ 146 \/ 221 \/ 463 \/ 705 \/ 826 \/ 1230 \/ 1835 \/ 3045 \/ 4255 \/ 5465 \/ 3710 \/ 4315 \/ 6130 \/ 6735 \/ 7945 \/ 9155 \/ 10365 \/ 10970 \/ 12785 \/ 13390 \/ 15205 \/ 15810 \/ 18230 \/ 18835 \/ 20045 \/ 21255 2*\/ 610 3*\/ 38 3*\/ 345 3*\/ 1555 7*\/ 335 18*\/ 15 ---- + ------- + ------- + ------- + ------- + ------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + -------- + --------- + ---------- + --------- + --------- 25 5 10 10 10 10 25 25 25 25 25 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 25 10 50 50 50 25
$$\frac{3 \sqrt{345}}{50} + \frac{\sqrt{3710}}{50} + \frac{\sqrt{4315}}{50} + \frac{\sqrt{1230}}{25} + \frac{\sqrt{221}}{10} + \frac{\sqrt{6130}}{50} + \frac{\sqrt{6735}}{50} + \frac{\sqrt{1835}}{25} + \frac{\sqrt{7945}}{50} + \frac{3 \sqrt{38}}{10} + \frac{\sqrt{9155}}{50} + \frac{2 \sqrt{610}}{25} + \frac{\sqrt{10365}}{50} + \frac{\sqrt{10970}}{50} + \frac{\sqrt{463}}{10} + \frac{\sqrt{3045}}{25} + \frac{\sqrt{12785}}{50} + \frac{\sqrt{13390}}{50} + \frac{3 \sqrt{1555}}{50} + \frac{\sqrt{146}}{5} + \frac{\sqrt{15205}}{50} + \frac{\sqrt{15810}}{50} + \frac{7 \sqrt{335}}{50} + \frac{\sqrt{4255}}{25} + \frac{\sqrt{705}}{10} + \frac{\sqrt{18230}}{50} + \frac{\sqrt{18835}}{50} + \frac{18 \sqrt{15}}{25} + \frac{\sqrt{20045}}{50} + \frac{\sqrt{826}}{10} + \frac{\sqrt{21255}}{50} + \frac{\sqrt{5465}}{25} + \frac{1592}{25}$$
1592/25 + sqrt(146)/5 + sqrt(221)/10 + sqrt(463)/10 + sqrt(705)/10 + sqrt(826)/10 + sqrt(1230)/25 + sqrt(1835)/25 + sqrt(3045)/25 + sqrt(4255)/25 + sqrt(5465)/25 + sqrt(3710)/50 + sqrt(4315)/50 + sqrt(6130)/50 + sqrt(6735)/50 + sqrt(7945)/50 + sqrt(9155)/50 + sqrt(10365)/50 + sqrt(10970)/50 + sqrt(12785)/50 + sqrt(13390)/50 + sqrt(15205)/50 + sqrt(15810)/50 + sqrt(18230)/50 + sqrt(18835)/50 + sqrt(20045)/50 + sqrt(21255)/50 + 2*sqrt(610)/25 + 3*sqrt(38)/10 + 3*sqrt(345)/50 + 3*sqrt(1555)/50 + 7*sqrt(335)/50 + 18*sqrt(15)/25
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