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(-1)^n*sqrt(n)/(n+100)

  • How to use it?

  • Sum of series:
  • ((-1)^(n+1))/n ((-1)^(n+1))/n
  • sin(n) sin(n)
  • (-1)^n*sqrt(n)/(n+100) (-1)^n*sqrt(n)/(n+100)
  • (0.15/0.05)^1.3 (0.15/0.05)^1.3

  • Identical expressions

  • (- one)^n*sqrt(n)/(n+ one hundred)
  • ( minus 1) to the power of n multiply by square root of (n) divide by (n plus 100)
  • ( minus one) to the power of n multiply by square root of (n) divide by (n plus one hundred)
  • (-1)^n*√(n)/(n+100)
  • (-1)n*sqrt(n)/(n+100)
  • -1n*sqrtn/n+100
  • (-1)^nsqrt(n)/(n+100)
  • (-1)nsqrt(n)/(n+100)
  • -1nsqrtn/n+100
  • -1^nsqrtn/n+100
  • (-1)^n*sqrt(n) divide by (n+100)

  • Similar expressions

  • (1)^n*sqrt(n)/(n+100)
  • (-1)^n*sqrt(n)/(n-100)
Sum of series/ (-1)^n*sqrt(n)/(n+100)

Sum of series (-1)^n*sqrt(n)/(n+100)


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The solution

You have entered [src] 
  oo             
____             
\   `            
 \        n   ___
  \   (-1) *\/ n 
  /   -----------
 /      n + 100  
/___,            
n = 1
$$\sum_{n=1}^{\infty} \frac{\left(-1\right)^{n} \sqrt{n}}{n + 100}$$ 
Sum(((-1)^n*sqrt(n))/(n + 100), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{\left(-1\right)^{n} \sqrt{n}}{n + 100}$$
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
$$a_{n} = \frac{\sqrt{n}}{n + 100}$$
and
$$x_{0} = 1$$
,
$$d = 1$$
,
$$c = 0$$
then
$$R = \tilde{\infty} \left(1 + \lim_{n \to \infty}\left(\frac{\sqrt{n} \left(n + 101\right)}{\sqrt{n + 1} \left(n + 100\right)}\right)\right)$$
Let's take the limit
we find
False
The rate of convergence of the power series
The answer [src] 
  oo             
____             
\   `            
 \        n   ___
  \   (-1) *\/ n 
  /   -----------
 /      100 + n  
/___,            
n = 1
$$\sum_{n=1}^{\infty} \frac{\left(-1\right)^{n} \sqrt{n}}{n + 100}$$ 
Sum((-1)^n*sqrt(n)/(100 + n), (n, 1, oo))
The graph
Sum of series (-1)^n*sqrt(n)/(n+100)

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