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07.04 Mathematical Induction

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Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.
(4 points each.)

  1. 4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + … + 4n( 4n + 2) = quantity four times quantity four n plus one times quantity eight n plus seven divided all divided by six
  2. 12 + 42 + 72 + … + (3n – 2)2 = quantity n times quantity six n squared minus three n minus one all divided by two

For the given statement Pn, write the statements P1, Pk, and Pk+1.
(2 points)

  1. 2 + 4 + 6 + . . . + 2n = n(n+1)

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