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 +na^n-lb.

d) If a ≠ 0, then

for all n ∈ N.

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