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Prove that 1 13 + 1 35 + 1 57 + + 1 (2n1)(2n+1) = n 2n+1 for every positive integer n

Chapter 4, Problem 2

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QUESTION:

Prove that 1 13 + 1 35 + 1 57 + + 1 (2n1)(2n+1) = n 2n+1 for every positive integer n.

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QUESTION:

Prove that 1 13 + 1 35 + 1 57 + + 1 (2n1)(2n+1) = n 2n+1 for every positive integer n.

ANSWER:

Step 1 of 3

Mathematical induction works with 2 steps:

     1.  Basis step: prove that the statement is true for the base case.

     2.  Inductive step: Assume that the statement is true for some positive integer . Then prove that it is true for some positive integer .

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