Write the first four terms of the sequences

Chapter 5, Problem 7E

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QUESTION:

Let \(a_{k} = 2k + 1 and b_{k} = (k − 1)^{3} + k + 2\) for all integers k ≥ 0. Show that the first three terms of these sequences are identical but that their fourth terms differ.

Text Transcription:

a_k = 2k + 1 and b_k = (k − 1)^3 + k + 2

Questions & Answers

QUESTION:

Let \(a_{k} = 2k + 1 and b_{k} = (k − 1)^{3} + k + 2\) for all integers k ≥ 0. Show that the first three terms of these sequences are identical but that their fourth terms differ.

Text Transcription:

a_k = 2k + 1 and b_k = (k − 1)^3 + k + 2

ANSWER:

Solution

Given Let  = 2k + 1 and  = (k – 1 )3 + k + 2 for all integers k ≥ 0.

i.e. k=0,1,2,3,4,.......n

To Show that the first three terms of these sequences are identical but that their fourth terms differ.

The first four terms of the given sequence are shown below

Value of n

= 2k + 1

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