Question

Use the limit theorems (e.g., algebraic limit theorems, squeeze theorem, etc.) and the standard null sequences from class to determine if the following sequences converge or diverge. For those that converge, find their limit.

(n²-1)/(2n³-3n)

Answer 1

The sequence converges to 0.

Step-by-step explanation:

To determine if the sequence converges or diverges, let's analyze the terms of the sequence.

For large values of n, the leading term of the numerator is n^2, and the leading term of the denominator is 2n^3. As n approaches infinity, the leading term of the numerator dominates, and the sequence becomes equivalent to n^2 / 2n^3.

Simplifying further, we get 1 / (2n). As n approaches infinity, this term converges to 0. Therefore, the sequence converges to 0.