Question

Determine whether the sequence is convergent or divergent. If it is convergent, find the limit. (If the quantity diverges, enter DIVERGES.) an=(5n²+n-1)/n²

A) Convergent with a limit
B) Convergent with no limit
C) Divergent
D) DIVERGES

Answer 1

The sequence (5n^2 + n - 1)/n^2 is convergent with the limit as n approaches infinity being 5.

Step-by-step explanation:

To determine whether the sequence an = (5n2 + n - 1)/n2 is convergent or divergent, we look at the limit of the sequence as n approaches infinity. We find the limit by dividing each term in the numerator by n2.

Limit as n → ∞:
= limn→∞ (5n2/n2 + n/n2 - 1/n2)
= limn→∞ (5 + 1/n - 1/n2)
= 5 + 0 - 0
= 5
Since the limit is a finite number, the sequence is convergent and the limit is 5.