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[M] Prove each of the following for all positive integers n using mathematical induction (a) 1+ 3 +5 +...+(2n-1) = n(2n-1)(2n +1) 3 (b)

[M] Prove each of the following for all positive integers \( n \) using mathematical induction (a) \( 1^{2}+3^{2}+5^{2}+\ldot 

[M] Prove each of the following for all positive integers n using mathematical induction (a) 1+ 3 +5 +...+(2n-1) = n(2n-1)(2n +1) 3 (b) i(2) 2+ (n 1)2n+1 n i=1 (c) 2+4 +6+...+ 2n = n+ n

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