Sequences Exercises

Answer

This sequence is like  except there's even more stuff in the denominator. This sequence converges to 0.

Answer

This sequence diverges. As n approaches ∞, the terms get farther and farther apart.

Answer

Since the terms are all 7, this sequence converges to 7.

Answer

Following the hint, the n^th term of this sequence looks like

The factors in the denominator cancel with factors in the numerator, leaving

As n approaches ∞, the terms a_n also approach ∞, so this sequence diverges.

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.