27–34. Working with sequences Several terms of a sequence {aₙ}ₙ₌₁∞ are given.
c. Find an explicit formula for the nth term of the sequence.


{-5, 5, -5, 5, ......}

67–70. Formulas for sequences of partial sums Consider the following infinite series.

c.Make a conjecture for the value of the series.

∑⁽∞⁾ₖ₌₁2⁄[(2k − 1)(2k + 1)]

Explain why or why not

Determine whether the following statements are true and give an explanation or counterexample.

c.The convergent sequences {aₙ} and {bₙ} differ in their first 100 terms, but aₙ = bₙ for n > 100.

It follows that limₙ→∞aₙ = limₙ→∞bₙ.

{Use of Tech} Periodic dosing

Many people take aspirin on a regular basis as a preventive measure for heart disease. Suppose a person takes 80 mg of aspirin every 24 hours. Assume aspirin has a half-life of 24 hours; that is, every 24 hours, half of the drug in the blood is eliminated.

c.Assuming the sequence has a limit, confirm the result of part (b) by finding the limit of {dₙ} directly.

39–40. {Use of Tech} Lower and upper bounds of a series

For each convergent series and given value of n, use Theorem 10.13 to complete the following.

c. Find lower and upper bounds (Lₙ and Uₙ, respectively) for the exact value of the series.

39. ∑ (k = 1 to ∞) 1 / k⁷ ; n = 2

Explain why or why not

Determine whether the following statements are true and give an explanation or counterexample.

c.If the terms of the sequence {aₙ} are positive and increasing, then the sequence of partial sums for the series∑⁽∞⁾ₖ₌₁aₖ diverges.

27–34. Working with sequences Several terms of a sequence {aₙ}ₙ₌₁∞ are given.

c. Find an explicit formula for the nth term of the sequence.

{1, 3, 9, 27, 81, ......}