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Chapter 7: Q 46. (page 615)

Given that $a_{0} = - 3, a_{1} = 5, a_{2} = - 4, a_{3} = 2$ and ${鈭� a_{k}}_{k = 2}^{鈭�} = 7$ , find the value of ${鈭� a_{k}}_{k = 4}^{鈭�}$ .

Short Answer

Expert verified

The value of ${鈭� a_{k}}_{k = 4}^{鈭�}$ is 9.

Step by step solution

01

Step 1. Given information.

Given that $a_{0} = - 3, a_{1} = 5, a_{2} = - 4, a_{3} = 2$ and ${鈭� a_{k}}_{k = 2}^{鈭�} = 7$ .

02

Step 2. Express the series in terms of known values.

Value of ${鈭� a_{k}}_{k = 4}^{鈭�}$ can be obtained as follows.

$\begin{array}{rcl} {鈭� a_{k}}_{k = 4}^{鈭�} & = & {鈭� a_{k}}_{k = 2}^{鈭�} - (a_{2} + a_{3}) \\ = & 7 - (- 4 + 2) \\ = & 7 + 2 \\ = & 9 \end{array}$

Therefore, value of ${鈭�}_{k = 4}^{鈭�} a_{k}$ is 9.

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Most popular questions from this chapter

Given a series ${鈭�}_{k = 1}^{鈭�} a_{k}$ , in general the divergence test is inconclusive when . For a $a_{k} 鈫� 0$ geometric series, however, if the limit of the terms of the series is zero, the series converges. Explain why.

If $\lim_{k 鈫� 鈭�} \frac{a_{k}}{b_{k}} Where L i s$ a positive finite number, what may we conclude about the two series?

Use the divergence test to analyze the given series. Each answer should either be the series diverges or the divergence test fails, along with the reason for your answer.

${鈭�}_{k = 1}^{鈭�} \frac{k}{3 k^{2} + 100}$

What is meant by the remainder $R_{n}$ of a series ${鈭�}_{k = 1}^{鈭�} a_{k}$

Use the divergence test to analyze the given series. Each answer should either be the series diverges or the divergence test fails, along with the reason for your answer.

${鈭�}_{k = 1}^{鈭�} 鈥� {(\frac{k}{1 + k})}^{k^{2}}$

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