Question 6 Let (.) be a sequence of positive numbers with lim = L. Let 0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 63RE
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Question 6
Let (rn) be a sequence of positive numbers with
In+l = L.
lim
n 0 In
Let 0 < e < L. Show that there exists K EN such that
n2 K = A(L – e)" s In SB(L+e)".
Deduce that
lim r" = L.
Question 7
Assume the limit
(1+ +)" -
lim
= e.
Use the previous exercise to show that
lim n/ (n!)"/" =
= e.
Transcribed Image Text:Question 6 Let (rn) be a sequence of positive numbers with In+l = L. lim n 0 In Let 0 < e < L. Show that there exists K EN such that n2 K = A(L – e)" s In SB(L+e)". Deduce that lim r" = L. Question 7 Assume the limit (1+ +)" - lim = e. Use the previous exercise to show that lim n/ (n!)"/" = = e.
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