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Prove that 1 14 + 1 47 + 1 710 + + 1 (3n2)(3n+1) = n 3n+1 for every positive integer n

Chapter 4, Problem 3

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QUESTION:

Prove that 1 14 + 1 47 + 1 710 + + 1 (3n2)(3n+1) = n 3n+1 for every positive integer n.

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QUESTION:

Prove that 1 14 + 1 47 + 1 710 + + 1 (3n2)(3n+1) = n 3n+1 for every positive integer n.

ANSWER:

Step 1 of 3

By using the principles of mathematical induction, the given sum of the fraction can be proved. The principle of mathematical induction is stated as follows.

 for every positive integer , is true if the following satisfies.

     1.    is true

     2.   The statement  is true.

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