Mister Exam
Other calculators
- Taylor Series Step by Step
- Fourier series step by step
- Differential equations Step by Step
- Product of series
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How to use it?
- Sum of series:
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1/(n*(n+1))
- 1/n^p
- nx^(n!)
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1/((2*n+5)*(2*n+7))
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Identical expressions
- five *sin(sqrt(i* zero . two))/ twenty-five
- 5 multiply by sinus of ( square root of (i multiply by 0.2)) divide by 25
- five multiply by sinus of ( square root of (i multiply by zero . two)) divide by twenty minus five
- 5*sin(√(i*0.2))/25
- 5sin(sqrt(i0.2))/25
- 5sinsqrti0.2/25
- 5*sin(sqrt(i*0.2)) divide by 25
Sum of series 5*sin(sqrt(i*0.2))/25
The solution
You have entered
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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))
The rate of convergence of the power series
The answer
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/ ___\ / ____\ / ____\ / ____\ / ____\ / ____\ / ____\ / ____\ / ____\ / ____\ / _____\ / _____\ / _____\ / ___\ / ____\ / ____\ / ____\ / ___\ / ____\ / ___\
|\/ 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
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