Determine if the sequence converges or diverges. If the sequence converges, what does it converge to?
Answer
This sequence is like except there's even more stuff in the denominator. This sequence converges to 0.
Example 2
Determine if the sequence converges or diverges. If the sequence converges, what does it converge to?
an = 2n
Answer
This sequence diverges. As n approaches ∞, the terms get farther and farther apart.
Example 3
Determine if the sequence converges or diverges. If the sequence converges, what does it converge to?
an = 7
Answer
Since the terms are all 7, this sequence converges to 7.
Example 4
Determine if the sequence converges or diverges. If the sequence converges, what does it converge to?
(hint: expand the factorial)
Hint
Expand the factorial.
Answer
Following the hint, the nth term of this sequence looks like
The factors in the denominator cancel with factors in the numerator, leaving
As n approaches ∞, the terms an also approach ∞, so this sequence diverges.
Example 5
Determine if the sequence converges or diverges. If the sequence converges, what does it converge to?
Answer
The terms of this sequence bounce back and forth, getting farther away from zero. Since the terms aren't approaching any finite value, the sequence diverges.
except there's even more stuff in the denominator. This sequence converges to 0.
(hint: expand the factorial)
