. Use an induction argument to prove that: For all integers n 24, 2 Zn Proof:...

 

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. Use an induction argument to prove that: For all integers n 24, 2" Zn² Proof: We proceed by induction. Since 224², the inequality holds for n=4. Assume that 2K2 K² where K24. we show that 2*+¹ (k+₁) = K² +2k+l. observe that ₂K+¹= 2.2k 22K²= K²+K² K+K-KK²+4K 2 = K²+2k +2K2 K² +2k+8 > K²+2K+1= (K+1)² Therefore, 2K+ (K+1) ². By the Principle of Mathematical induction, 2"n² for every integer 124. . Use an induction argument to prove that: For all integers n 24, 2" Zn² Proof: We proceed by induction. Since 224², the inequality holds for n=4. Assume that 2K2 K² where K24. we show that 2*+¹ (k+₁) = K² +2k+l. observe that ₂K+¹= 2.2k 22K²= K²+K² K+K-KK²+4K 2 = K²+2k +2K2 K² +2k+8 > K²+2K+1= (K+1)² Therefore, 2K+ (K+1) ². By the Principle of Mathematical induction, 2"n² for every integer 124.