Mark cach statement Truc or False. Justify cach answer. (a) If lim s, =s and lim t, = t, then lim (s„,) = st. (b) If lim s, = +o, then (s„) is said to converge to +. (c) Given sequences (s,) and (1,) with s, < t, for all n e N, if lim s, = +0, then lim t, = +o. (d) Suppose (Sm) is a sequence such that the sequence of ratios (Sp+1/S,) converges to L. If L< 1, then lim s, = 0.
Mark cach statement Truc or False. Justify cach answer. (a) If lim s, =s and lim t, = t, then lim (s„,) = st. (b) If lim s, = +o, then (s„) is said to converge to +. (c) Given sequences (s,) and (1,) with s, < t, for all n e N, if lim s, = +0, then lim t, = +o. (d) Suppose (Sm) is a sequence such that the sequence of ratios (Sp+1/S,) converges to L. If L< 1, then lim s, = 0.
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:Mark cach statement True or False. Justify cach answer.
(a) If lim s, = s and lim t, = t, then lim (s,t,) = st.
(b) If lim s, =+o, then (s,) is said to converge to +o.
(c) Given sequences (s,) and (1,) with s, < t, for all n e N, if lim s,
then lim t,
+ 0,
%3D
=+ 00,
(d) Suppose (sn) is a sequence such that the sequence of ratios (Sn+1/Sn)
converges to L. If L < 1, then lim s, = 0.
%3D
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