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:
- n^2*x^n
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2(1/(n^2+5n+6))
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cosn/n
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1/((2^(k+1))-1)
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Identical expressions
- (sqrt(i- one)+sqrti)/2nsqrtn
- ( square root of (i minus 1) plus square root of i) divide by 2n square root of n
- ( square root of (i minus one) plus square root of i) divide by 2n square root of n
- (√(i-1)+√i)/2n√n
- sqrti-1+sqrti/2nsqrtn
- (sqrt(i-1)+sqrti) divide by 2nsqrtn
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Similar expressions
- (sqrt(i-1)-sqrti)/2nsqrtn
- (sqrt(i+1)+sqrti)/2nsqrtn
- (sqrt(i-1)+sqrti)/(2n*sqrtn)
Sum of series (sqrt(i-1)+sqrti)/2nsqrtn
The solution
You have entered
[src]
n ____ \ ` \ _______ ___ \ \/ i - 1 + \/ i ___ / -----------------*n*\/ n / 2 /___, i = 1
$$\sum_{i=1}^{n} \sqrt{n} n \frac{\sqrt{i} + \sqrt{i - 1}}{2}$$
Sum((((sqrt(i - 1) + sqrt(i))/2)*n)*sqrt(n), (i, 1, n))
The answer
[src]
n ____ \ ` \ / ___ ________\ \ 3/2 |\/ i \/ -1 + i | / n *|----- + ----------| / \ 2 2 / /___, i = 1
$$\sum_{i=1}^{n} n^{\frac{3}{2}} \left(\frac{\sqrt{i}}{2} + \frac{\sqrt{i - 1}}{2}\right)$$
Sum(n^(3/2)*(sqrt(i)/2 + sqrt(-1 + i)/2), (i, 1, n))
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