SOLUTION: Suppose in a proof of the summation formula 7 + 9 + 11 + ... + (2n + 5) = n(n + 6) by mathematical induction, you show the formula valid for n = 1 and assume that it is valid for n

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Question 1036870: Suppose in a proof of the summation formula 7 + 9 + 11 + ... + (2n + 5) = n(n + 6) 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?
7 + 9 + 11 + ... + (2k + 5) + (2(k+1) + 5) = k(k + 6) + (k+1)((k+1) + 6)
7 + 9 + 11 + ... + (2(k+1) + 5) = k(k + 6)
7 + 9 + 11 + ... + (2k + 5) = k(k + 6)
7 + 9 + 11 + ... + (2k + 5) + (2(k+1) + 5) = k(k + 6) + (2(k+1) + 5)
Answer by ikleyn(52781)   (Show Source):
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Suppose in a proof of the summation formula 7 + 9 + 11 + ... + (2n + 5) = n(n + 6) 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. 7 + 9 + 11 + ... + (2k + 5) + (2(k+1) + 5) = k(k + 6) + (k+1)((k+1) + 6)
2. 7 + 9 + 11 + ... + (2(k+1) + 5) = k(k + 6)
3. 7 + 9 + 11 + ... + (2k + 5) = k(k + 6)
4. 7 + 9 + 11 + ... + (2k + 5) + (2(k+1) + 5) = k(k + 6) + (2(k+1) + 5)
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#4.

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P.S. The method of the math induction is one of perfect and most brilliant methods,
but doing exercises like this one can only disgust students from the method (and from the Math itself).

If you want to learn the method of the math induction, learn it from other sources.

Among other appropriate sources see, for example, the lessons
    - Mathematical induction and arithmetic progressions
    - Mathematical induction and geometric progressions
    - Mathematical induction for sequences other than arithmetic or geometric
    - Proving inequalities by the method of Mathematical Induction
in this site.