Prove the following.
(a) If lim sn = +∞ and k > 0, then lim ksn = +∞.
(b) If lim sn = +∞ and k < 0, then lim sn = −∞.
(c) lim sn = +∞ iff lim (−sn) = −∞.
(d) If lim sn = +∞ and if (tn) is a bounded sequence, then lim (sn + tn) = +∞.
(e) If (sn) converges to L > 0 and lim tn = +∞, then lim (sntn) = +∞.
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