Show that if lim(Sn) = (+ infinity) and inf{(Tn:n is a natural number)} > (- inf

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Since lim(Sn) = (+ infinity), given any large M > 0, we can find k (a natural number) such that Sn > M for all n >= k. Now, we also know that inf{(Tn:n is a natural number)} > (- infinity). Thus we can find a lower bound for (Tn). We will call it L. Since L is a lower bound of (Tn), Tn >= L for all n. Since Tn >= L for all n, Sn + Tn >= Sn + L for all n. Now, given any large number M, we can find k (a natural number) such that Sn > M - L for all n >= k. Knowing that Sn > M- L for all n >= k., examine the following: Sn + Tn >= Sn + L > (M-L) + L = M Thus Sn + Tn > M for all n >= k Thus we have found k, such that Sn + Tn > M for all n >= k . So, lim(Sn + Tn) = (+ infinity).

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