Mark each statement True or False. Justify each answer. (a) If (sn) and (t„) are convergent sequences with s, → s and t, → t, then lim (s, + t„) = s +t and lim (s,t,,) = st. (b) If (sn) converges to s and s, > 0 for all n e N, then s > 0. (c) The sequence (s„) converges to s iff lim s, = s. (d) lim s, = +o iff lim (1/s,) = 0.
Mark each statement True or False. Justify each answer. (a) If (sn) and (t„) are convergent sequences with s, → s and t, → t, then lim (s, + t„) = s +t and lim (s,t,,) = st. (b) If (sn) converges to s and s, > 0 for all n e N, then s > 0. (c) The sequence (s„) converges to s iff lim s, = s. (d) lim s, = +o iff lim (1/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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![Mark each statement True or False. Justify each answer.
(a) If (sn) and (t,) are convergent sequences with s, → s and t, → t, then
lim (s,+ t,) = s +t and lim (s„tn) = st.
(b) If (sn) converges to s and s, > 0 for all n e N, then s > 0.
(c) The sequence (s„) converges to s iff lim s,
(d) lim s, = +∞ iff lim (1/s,) = 0.
= S.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34147f77-5d8c-4cdc-a0b9-3c7e017adeee%2F2118e894-592b-413c-9fa7-d65fb7acbb23%2Fffxsrm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Mark each statement True or False. Justify each answer.
(a) If (sn) and (t,) are convergent sequences with s, → s and t, → t, then
lim (s,+ t,) = s +t and lim (s„tn) = st.
(b) If (sn) converges to s and s, > 0 for all n e N, then s > 0.
(c) The sequence (s„) converges to s iff lim s,
(d) lim s, = +∞ iff lim (1/s,) = 0.
= S.
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