(Solution) - Decide which of the following statements are true and which -(2025 Original AI-Free Solution)

Paper Details

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