1. Use induction to prove Bernoulli’s inequality: If 1 + x > 0, then (1 + x) n ≥1 + n x for all n ∈ . 2. Prove that for all integers x ≥ 8, x can be written in the form 3m + 5n, where m and n are...


1. Use induction to prove Bernoulli’s inequality: If 1 + x > 0, then (1 + x)n
≥1 + n x for all n ∈
.


2. Prove that for all integers x ≥ 8, x can be written in the form 3m + 5n, where m and n are nonnegative integers


3. Consider the statement “For all integers x ≥ k, x can be written in the form 5m + 7n, where m and n are nonnegative integers.”


(a) Find the smallest value of k that makes the statement true.


(b) Prove the statement is true with k as in part (a).



May 05, 2022
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