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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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.
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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