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Chapter 7: Q. 49 (page 592)

Write each of the arithmetic sequences in Exercises 47–50 in the form ${c + d k}_{k = 0}^{\infty}$
$1, - 1, \dots$

Short Answer

Expert verified

The required form is ${1 - 2 k}_{k = 0}^{\infty}$

Step by step solution

01

Step 1. Given information.

The given series is $1, - 1, \dots$

02

Step 2. Required form.

On comparing the given series with ${c, c + d, c + 2 d, \dots}$ , we get,

$c = 1 c + d = - 1 = - 2$

Therefore,

${c + d k}_{k = 0}^{\infty} can be written as {1 - 2 k}_{k = 0}^{\infty} .$

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Most popular questions from this chapter

Use either the divergence test or the integral test to determine whether the series in Exercises 32–43 converge or diverge. Explain why the series meets the hypotheses of the test you select.

36. $\sum_{k = 1}^{\infty} \frac{k}{k^{2} + 3}$

Determine whether the series $\sum_{k = 0}^{\infty} \frac{5^{k + 1}}{{(- 6)}^{k}}$ converges or diverges. Give the sum of the convergent series.

In Exercises 48–51 find all values of p so that the series converges.

$\sum_{k = 2}^{\infty} \frac{1}{k {(\ln (k))}^{p}}$

Find the values of x for which the series $\sum_{K = 0}^{\infty} {(\sin x)}^{k}$ converges.

$I f \lim_{k \to \infty} \frac{a_{k}}{b_{k}} = \infty and \sum_{k = 1}^{\infty}_____Converges the n \sum_{k = 1}^{\infty}_____(converges / diverges) .$

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