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 )
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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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