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Solve: The Inductive Hypothesis

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Let P (n) be the statement that 1^3 + 2^3 + â?¦ +n^3=(n(n+1)/2)^2 for the positive integer n.

a. What is the statement P(1)?
b. Show that P(1) is true, completing the basis step of that proof.
c. What is the inductive hypothesis?
d. What do you need to prove in the inductive step?
e. Complete the inductive step.
f. Explain why these steps show that this formula is true whenever n is a positive integer.

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Solution Summary

This solution is comprised of a very detailed, step-by-step response which illustrates how to find the inductive hypothesis and complete the required tasks for the given statement. Two files are attached, one in Word format and the other in pdf format. Both files are identical in content and provide the full solution.

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