Mister Exam

Other calculators


sqrt(n+1)/(n^2+ln^2n)
  • How to use it?

  • Sum of series:
  • 1/(n(n+1)(n+2)) 1/(n(n+1)(n+2))
  • 1/n^3 1/n^3
  • (5^n-2^n)/10^n (5^n-2^n)/10^n
  • 1/(n*ln(n)) 1/(n*ln(n))
  • Identical expressions

  • sqrt(n+ one)/(n^ two +ln^2n)
  • square root of (n plus 1) divide by (n squared plus ln squared n)
  • square root of (n plus one) divide by (n to the power of two plus ln squared n)
  • √(n+1)/(n^2+ln^2n)
  • sqrt(n+1)/(n2+ln2n)
  • sqrtn+1/n2+ln2n
  • sqrt(n+1)/(n²+ln²n)
  • sqrt(n+1)/(n to the power of 2+ln to the power of 2n)
  • sqrtn+1/n^2+ln^2n
  • sqrt(n+1) divide by (n^2+ln^2n)
  • Similar expressions

  • sqrt(n-1)/(n^2+ln^2n)
  • sqrt(n+1)/(n^2-ln^2n)

Sum of series sqrt(n+1)/(n^2+ln^2n)



=

The solution

You have entered [src]
  oo              
____              
\   `             
 \       _______  
  \    \/ n + 1   
   )  ------------
  /    2      2   
 /    n  + log (n)
/___,             
n = 1             
$$\sum_{n=1}^{\infty} \frac{\sqrt{n + 1}}{n^{2} + \log{\left(n \right)}^{2}}$$
Sum(sqrt(n + 1)/(n^2 + log(n)^2), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{\sqrt{n + 1}}{n^{2} + \log{\left(n \right)}^{2}}$$
It is a series of species
$$a_{n} \left(c x - x_{0}\right)^{d n}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}$$
In this case
$$a_{n} = \frac{\sqrt{n + 1}}{n^{2} + \log{\left(n \right)}^{2}}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\sqrt{n + 1} \left(\left(n + 1\right)^{2} + \log{\left(n + 1 \right)}^{2}\right)}{\sqrt{n + 2} \left(n^{2} + \log{\left(n \right)}^{2}\right)}\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The graph
Sum of series sqrt(n+1)/(n^2+ln^2n)

    Examples of finding the sum of a series