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Prove all numbers of the form: 8n² ± 6n + 1?
Prove all numbers of the form:
8n² ± 6n + 1
is a triangular number and can be expressed as a difference of two squares in two different ways.
1 Answer
- nyc_kidLv 76 years agoFavorite Answer
To show triangular number, one has to show that 8n² ± 6n + 1 can be expressed as k(k+1)/2 for some integer k.
For 8n² + 6n + 1 set k = 4n + 2, and for 8n² - 6n + 1 set k = 8n -1.
Expressing it as a difference of two squares, note, 8n² ± 6n + 1 = 9n² ± 6n + 1 - n² = (3n ± 1)² - n².
