# How do you use the Comparison Test to see if #1/(4n^2-1)# converges, n is going to infinity?

By signing up, you agree to our Terms of Service and Privacy Policy

To use the Comparison Test to determine the convergence of the series ( \sum \frac{1}{4n^2 - 1} ) as ( n ) approaches infinity:

- Consider the series ( \sum \frac{1}{4n^2} ).
- Observe that ( \frac{1}{4n^2} ) is a term of the harmonic series, which is known to diverge.
- Note that ( 4n^2 - 1 > 4n^2 ) for all positive integers ( n ).
- Utilize the Comparison Test, stating that if ( a_n ) is less than or equal to ( b_n ) for all ( n ) and ( \sum b_n ) converges, then ( \sum a_n ) converges.
- Since ( \frac{1}{4n^2 - 1} < \frac{1}{4n^2} ) for all positive integers ( n ), and ( \sum \frac{1}{4n^2} ) diverges, ( \sum \frac{1}{4n^2 - 1} ) must also diverge.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- If #f(9)=9# and #f^'(9)=4#, then what is the value of #lim_(x to9)(sqrt(f(x))-3)/(sqrtx -3)?#
- How do you test the series #Sigma (n+3)/(n(n+1)(n-2))# from n is #[3,oo)# for convergence?
- How do you determine if series #1/n!# converge or diverge with comparison test?
- How do you use the Integral test on the infinite series #sum_(n=1)^oo1/(2n+1)^3# ?
- Why does the Harmonic Series diverge?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7