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In Exercises 31–36 provide the first five terms of the given sequence. Unless specified, assume that the first term has index 1.

1-(-1)kk

Short Answer

Expert verified

The first five terms are2,0,23,0,25.

Step by step solution

01

Step 1. Given information.

The given sequence is1-(-1)kk.

02

Step 2. First term.

The generals sequence will be,

ak=1-(-1)kkk=1,a1=1-(-1)k=2

03

Step 3. Remaining terms.

Now put,

k=2,a2=1-(-1)2k=0k=3,a3=1-(-1)33=23k=4,a4=1-(-1)44=0k=5,a5=1-(-1)55=25

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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 Given Exercises converge or diverge. Explain why the series meets the hypotheses of the test you select.

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(Hint: Make a new recurrence by using two steps of the one given.)

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True/False:

Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.

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(b) True or False: If k=1akconverges, then ak0.

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(d) True or False: The harmonic series converges.

(e) True or False: If p>1, the series k=1k-pconverges.

(f) True or False: If f(x)0as x, then k=1f(k) converges.

(g) True or False: If k=1f(k)converges, then f(x)0as x.

(h) True or False: If k=1ak=Land {Sn}is the sequence of partial sums for the series, then the sequence of remainders {L-Sn}converges to 0.

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