Decide which of the following statements are true and which are false. Prove the true ones and
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Decide which of the following statements are true and which are false. Prove the true ones and give counterexamples to the false ones.
a) If a > 0 and b ≠ 0, then (a + b)n > bn for all n ∈ N.
b) If a < 0 < b, then (a + b)n < bn for all n ∈ N.
c) If n ∈ N is even and both a and b are negative, then (a + b)n > an +nan-lb.
d) If a ≠ 0, then
for all n ∈ N.
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a False If a b 1 and n 2 then a b n 0 is NOT greater than b ...View the full answer
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