Decide which of the following statements are true and which are false. Prove the true ones...

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.

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b) If a < 0 < b, then (a + b)n ≤ bn for all n ∈ N.

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c) If n ∈ N is even and both a and b are negative, then (a + b)n > an + nan−1b.

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d) If a ≠ 0, then

for all n ∈ N.