Convergence Test for Series with Square Root Terms

In summary, the conversation involves using the Comparison Test and Limit Comparison Test to determine the convergence or divergence of the series (summation n=1 to infinity) sqrt(n+2)/(2n^2+n+1). The individual has attempted to compare the series with different expressions, but is unsure why the inequality sign changes when plugging in a specific number. Another suggestion is made to try a different comparison using sqrt(n+n)/(2n^2).
  • #1
lha08
164
0

Homework Statement


Using Comparison test and LCT, determine whether it is convergent or divergent:

(summation n=1 to infinity) sqrt(n+2)/(2n^2+n+1)



Homework Equations





The Attempt at a Solution


i compared it with sqrt(x)/2n^2 which is 1/2n^(3/2)
and then the answer showed something weird...they had to plug in a number (e.g. 1) which reversed the inequality sign... to sqrt(n+2)/(2n^2+n+1) is larger than 1/2n^(3/2)...does anyone know why?
 
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  • #2


Then pick a different comparison. You want to make the numerator larger and the denominator smaller if you think it converges. Be creative! How about comparing with sqrt(n+n)/(2n^2)?
 

1. What is a series in math?

A series in math is a sequence of numbers that are added together in a specific order. It can also be described as the sum of an infinite number of terms.

2. How do I solve a series homework problem?

To solve a series homework problem, first identify the pattern or formula for the series. Then, plug in the given values into the formula and simplify to find the sum of the series.

3. What are some common types of series?

Some common types of series include arithmetic series, geometric series, and harmonic series. These series have different patterns and formulas for finding their sums.

4. Are there any shortcuts or tricks for solving series problems?

Yes, there are some shortcuts or tricks that can be used to solve certain types of series problems. These include using telescoping sums, the geometric series formula, or the sum of squares/cubes formulas. However, it is important to understand the underlying concepts and patterns before relying on these shortcuts.

5. How can I check if my series solution is correct?

To check if your series solution is correct, you can use a calculator or computer program to calculate the sum of the series. You can also try plugging in the given values into your formula to see if it produces the same result. Additionally, you can check your solution with a classmate or teacher.

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