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sqrt((i+2)/(i^3))

  • How to use it?

  • Sum of series:
  • ((-1)^(n+1))/n ((-1)^(n+1))/n
  • sin(n) sin(n)
  • ((-1)^n)*((x^n)/(2n*n!))
  • 9/(9n^2+21n-8) 9/(9n^2+21n-8)

  • Identical expressions

  • sqrt((i+ two)/(i^ three))
  • square root of ((i plus 2) divide by (i cubed ))
  • square root of ((i plus two) divide by (i to the power of three))
  • √((i+2)/(i^3))
  • sqrt((i+2)/(i3))
  • sqrti+2/i3
  • sqrt((i+2)/(i³))
  • sqrt((i+2)/(i to the power of 3))
  • sqrti+2/i^3
  • sqrt((i+2) divide by (i^3))

  • Similar expressions

  • sqrt((i-2)/(i^3))
Sum of series/ sqrt((i+2)/(i^3))

Sum of series sqrt((i+2)/(i^3))


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The solution

You have entered [src] 
  23              
____              
\   `             
 \         _______
  \       / i + 2 
   )     /  ----- 
  /     /      3  
 /    \/      i   
/___,             
i = 1
$$\sum_{i=1}^{23} \sqrt{\frac{i + 2}{i^{3}}}$$ 
Sum(sqrt((i + 2)/i^3), (i, 1, 23))
The rate of convergence of the power series
The answer [src] 
  ___     ____     ___     ____     ____     ____     ____     ____     ____     ____     _____     _____     _____     _____     _____     _____     _____       ___       ____        ___        ___
\/ 6    \/ 15    \/ 5    \/ 35    \/ 11    \/ 14    \/ 30    \/ 10    \/ 42    \/ 33    \/ 143    \/ 195    \/ 110    \/ 255    \/ 323    \/ 399    \/ 483    3*\/ 7    5*\/ 23    10*\/ 3    35*\/ 2 
----- + ------ + ----- + ------ + ------ + ------ + ------ + ------ + ------ + ------ + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + -------- + -------- + --------
  8       9        16      25       27       49       50       54       72      121       121       169       200       225       289       361       441        49       529         9          64
$$\frac{5 \sqrt{23}}{529} + \frac{\sqrt{33}}{121} + \frac{\sqrt{483}}{441} + \frac{\sqrt{110}}{200} + \frac{\sqrt{399}}{361} + \frac{\sqrt{10}}{54} + \frac{\sqrt{323}}{289} + \frac{\sqrt{255}}{225} + \frac{\sqrt{14}}{49} + \frac{\sqrt{195}}{169} + \frac{\sqrt{42}}{72} + \frac{\sqrt{143}}{121} + \frac{\sqrt{30}}{50} + \frac{\sqrt{11}}{27} + \frac{\sqrt{5}}{16} + \frac{3 \sqrt{7}}{49} + \frac{\sqrt{35}}{25} + \frac{\sqrt{6}}{8} + \frac{\sqrt{15}}{9} + \frac{35 \sqrt{2}}{64} + \frac{10 \sqrt{3}}{9}$$ 
sqrt(6)/8 + sqrt(15)/9 + sqrt(5)/16 + sqrt(35)/25 + sqrt(11)/27 + sqrt(14)/49 + sqrt(30)/50 + sqrt(10)/54 + sqrt(42)/72 + sqrt(33)/121 + sqrt(143)/121 + sqrt(195)/169 + sqrt(110)/200 + sqrt(255)/225 + sqrt(323)/289 + sqrt(399)/361 + sqrt(483)/441 + 3*sqrt(7)/49 + 5*sqrt(23)/529 + 10*sqrt(3)/9 + 35*sqrt(2)/64
Numerical answer [src] 
4.99514234589580603682599008185
4.99514234589580603682599008185
The graph
Sum of series sqrt((i+2)/(i^3))

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