6. Prove that each of the following inequalities holds for all n E N. (a) n <...
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6. Prove that each of the following inequalities holds for all n E N.
(a) n < 2n.
(b) n2 ~ 2n + 1.
(c) n3 ~ 3n .
[!]. This exercise is used in Section 2.3. Prove that 0 ~ a < b implies o ~ an < bn and 0 ~ y'a < V'b for all n E N.
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