Determine if the sequence converges or diverges. If the sequence converges, what does it converge to?
This sequence is like except there's even more stuff in the denominator. This sequence converges to 0.
an = 2n
This sequence diverges. As n approaches ∞, the terms get farther and farther apart.
an = 7
Since the terms are all 7, this sequence converges to 7.
(hint: expand the factorial)
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.
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.
Make it rain.