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For n 2:: 2, verify the following relations between the pentagonal, square, and

Chapter 2, Problem 11

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QUESTION:

For n 2:: 2, verify the following relations between the pentagonal, square, and triangularnumbers:(a) Pn = tn-l + n2(b) Pn = 3tn-l + n = 2tn-l + tn

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QUESTION:

For n 2:: 2, verify the following relations between the pentagonal, square, and triangularnumbers:(a) Pn = tn-l + n2(b) Pn = 3tn-l + n = 2tn-l + tn

ANSWER:

Step 1 of 3

In the preceding tasks was proven that for each positive integer  the triangular numbers are given by formula

...(1)

and the pentagonal numbers are given by formula

...(2)

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