Establish the formulas below by mathematical induction:
(a) for all n ≥ 1.
(b) 1 + 3 + 5 + ··· + (2n − 1) = n2 for all n ≥ 1.
(c) for all n ≥ 1.
(d) for all n ≥ 1.
(e) .
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