Expressing Consecutive Squares and Cubes

 

Expressing consecutive squares:

n(n + 1) \; + \; (n + 1) \; = \; (n + 1)^2

(0 * 1) \; + \; 1 \; = \; 1^2
(1 * 2) \; + \; 2 \; = \; 2^2
(2 * 3) \; + \; 3 \; = \; 3^2
(3 * 4) \; + \; 4 \; = \; 4^2
(4 * 5) \; + \; 5 \; = \; 5^2
………………………………….
………………………………….

 

Expressing consecutive cubes

n(n + 1)(n + 2) \; + \; (n + 1) \; = \; (n + 1)^3

(0 * 1 * 2) \; + \; 1 \; = \; 1^3
(1 * 2 * 3) \; + \; 2 \; = \; 2^3
(2 * 3 * 4) \; + \; 3 \; = \; 3^3
(3 * 4 * 5) \; + \; 4 \; = \; 4^3
(4 * 5 * 6) \; + \; 5 \; = \; 5^3
…………………………………….
…………………………………….

 
Can you express consecutive 4-th powers?
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged , . Bookmark the permalink.

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