42. Let e = 1+ 1/1! + 1/2! + 1/3! + Show that if k is a positive integer, then kle is not an integer. (Hint: Show that (k+ 1)-1 + (k + 1)-1(k + 2)-1 + (k +1)-1(k +2)-(k+3)-l+..<1 by comparing the expression on the left to a geometric series )

42. Let e = 1+ 1/1! + 1/2! + 1/3! + Show that if k is a positive integer, then kle is not an integer. (Hint: Show that (k+ 1)-1 + (k + 1)-1(k + 2)-1 + (k +1)-1(k +2)-(k+3)-l+..<1 by comparing the expression on the left to a geometric series )

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.4: Prime Factors And Greatest Common Divisor

Problem 4E: Find the smallest integer in the given set. { and for some in } { and for some in }

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Please solve this

42. Let e = 1+1/1! + 1/2! + 1/3! +.... Show that if k is a positive integer,
then kle is not an integer. (Hint: Show that (k+ 1)-1 + (k + 1)-1(k +
2)-1+ (k+1)-(k +2)-(k+3)-1+ ...<1 by comparing the expression
on the left to a geometric series.)

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