Problem

Show that hn = t2n − 1. for all positive integers n where hn is the nth hexagonal number,...

Show that hn = t2n − 1. for all positive integers n where hn is the nth hexagonal number, defined in Exercise, and t2n − 1 is the (2n − 1)st triangular number.

Exercise

a) Define the hexagonal numbers hn for n = 1, 2, . . . in a manner analogous to the definitions of triangular, square, and pentagonal numbers. (Recall that a hexagon is a six-sided polygon.)

b) Find a closed formula for hexagonal numbers.

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Solutions For Problems in Chapter 1.2