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Let n >1. A hexagonal number h, is of the form h, = n(2n – 1). - a. Determine the first 5 hexagonal numbers. b. Illustrate the first 5 hexagonal numbers. c. Define h, recursively. d. If p, and t,-1 are nth pentagonal and (n-1)th triangular numbers, respectively, then prove directly that pn + tp-1 = hn.

Let n >1. A hexagonal number h, is of the form h, = n(2n – 1). - a. Determine the first 5 hexagonal numbers. b. Illustrate the first 5 hexagonal numbers. c. Define h, recursively. d. If p, and t,-1 are nth pentagonal and (n-1)th triangular numbers, respectively, then prove directly that pn + tp-1 = hn.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let n > 1. A hexagonal number h, is of the form h, = n(2n – 1). | a. Determine the first 5 hexagonal numbers. b. Illustrate the first 5 hexagonal numbers. c. Define h, recursively. d. If p, and tr-1 are nth pentagonal and (n- 1)th triangular numbers, respectively, then prove | directly that pn + tn-1 = hn.
Transcribed Image Text:Let n > 1. A hexagonal number h, is of the form h, = n(2n – 1). | a. Determine the first 5 hexagonal numbers. b. Illustrate the first 5 hexagonal numbers. c. Define h, recursively. d. If p, and tr-1 are nth pentagonal and (n- 1)th triangular numbers, respectively, then prove | directly that pn + tn-1 = hn.
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