SOLUTION: Suppose in a proof of the summation formula 1 + 5 + 9 + ... + (4n - 3) = n(2n - 1) by mathematical induction, you show the formula valid for n = 1 and assume that it is valid for n

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Question 1035624: Suppose in a proof of the summation formula 1 + 5 + 9 + ... + (4n - 3) = n(2n - 1) by mathematical induction, you show the formula valid for n = 1 and assume that it is valid for n = k. What is the next equation in the induction step of this proof?
1 + 5 + 9 + ... + (4k - 3) = k(2k - 1) + (4(k+1) - 3)
1 + 5 + 9 + ... + (4k - 3) + (4(k+1) - 3) = k(2k - 1) + (4(k+1) - 3)
1 + 5 + 9 + ... + (4k - 3) + (4(k+1) - 3) = k(2k - 1) + (k + 1)[2(k + 1) - 1]
1 + 5 + 9 + ... + (4k - 3) = k(2k - 1)
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
From the second line of the proof...
1 + 5 + 9 + ... + (4k - 3) + (4(k+1) - 3) = k(2k - 1) + (4(k+1) - 3)
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