Exercice à rédiger en anglais... Kevin notes that : 5^2 - 4^2 = 5+4 ; 10^2 - 9^2 = 10+9 ; 250^2 - 249^2 = 250+249 and thus, he asserts that the difference between the squares of two consecutive numbers is equal to the sum of this two consecutive numbers. Mary tells him his conjecture couldn't be right for any consecutive numbers. How can Kevin prove he's right ?

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2012-11-24T17:23:08+01:00

(n+1)^2 - n^2 = n+1+n

so n^2+2n+1-n^2 = 2n+1

so 2n+1=2n+1

 

Kevin is right!!