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Suppose You Wish to Prove That the Following Is True

Question 42

Short Answer

Suppose you wish to prove that the following is true for all positive integers n by using the Principle of Mathematical Induction: 1+3+5+...+(2 n-1)=n2 .
(a) Write P(1)
(b) Write P(72)
(c) Write P(73)
(d) Use P(72) to prove P(73)
(e) Write P(k)
(f) Write P(k+1)
(g) Use the Principle of Mathematical Induction to prove that P(n) is true for all positive integers n

Correct Answer:

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(a) 1=12 .
(b) 1+3+5+...+143=722 .
(c)

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