# Prove that lim_(n->oo) (2n+1)/(3n+2)=2/3 ?

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

To prove that ( \lim_{n \to \infty} \frac{2n + 1}{3n + 2} = \frac{2}{3} ), we can use the limit properties and algebraic manipulation.

First, we divide both the numerator and the denominator by the highest power of ( n ), which is ( n ) in this case:

[ \lim_{n \to \infty} \frac{2n + 1}{3n + 2} = \lim_{n \to \infty} \frac{\frac{2n}{n} + \frac{1}{n}}{\frac{3n}{n} + \frac{2}{n}} ]

This simplifies to:

[ \lim_{n \to \infty} \frac{2 + \frac{1}{n}}{3 + \frac{2}{n}} ]

As ( n ) approaches infinity, ( \frac{1}{n} ) and ( \frac{2}{n} ) approach zero. Therefore, the limit becomes:

[ \frac{2 + 0}{3 + 0} = \frac{2}{3} ]

Thus, we have proven that ( \lim_{n \to \infty} \frac{2n + 1}{3n + 2} = \frac{2}{3} ).

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.

- How to choose the Bn for limit comparison test?
- How do you use the integral test to determine whether #int x^-x# converges or diverges from #[1,oo)#?
- How do you use the limit comparison test to determine if #Sigma n/(n^2+1)# from #[1,oo)# is convergent or divergent?
- How do you determine convergence or divergence for the summation of #n*e^(-n/2)# using the integral test how do you answer?
- Does #a_n=x^n/(n!) # converge for any x?

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