Show that if an denotes the nth positive integer that is

Chapter 1, Problem 27E

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QUESTION:

Show that if \(a_{n}\) denotes the \(n\)th positive integer that is not a perfect square, then \(a_{n}=n+\{\sqrt{n}\}\), where \(\{x\}\) denotes the integer closest to the real number \(x\).

Equation Transcription:

Text Transcription:

a_n = n+ { sqrt n}  

{x}  

x

Questions & Answers

QUESTION:

Show that if \(a_{n}\) denotes the \(n\)th positive integer that is not a perfect square, then \(a_{n}=n+\{\sqrt{n}\}\), where \(\{x\}\) denotes the integer closest to the real number \(x\).

Equation Transcription:

Text Transcription:

a_n = n+ { sqrt n}  

{x}  

x

ANSWER:

Solution:

Step1:

In this problem, we have to show that an=n+{where {x} denotes the integer closest to the real number x  where an denotes the nth positive integer that is not a perfect square then.

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