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Suppose You Wish to Prove That the Following Is True

Question 31

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Suppose you wish to prove that the following is true for all positive integers n by using 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 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) 1+3+5+.

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