"Lena has 2 consecutive integers. She notices that their sum is equal to the difference between their squares. Lena picks another 2 consecutive integers and notices the same thing. Prove algebraically that this is true for any 2 consecutive integers?

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Answer 1 · 2018-04-13T13:03:52

Kindly refer to the Explanation.

Recall that the consecutive integers differ by #1#.

Hence, if #m# is one integer, then, the succeeding integer

must be #n+1#.

The sum of these two integers is #n+(n+1)=2n+1#.

The difference between their squares is #(n+1)^2-n^2#,

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

#=2n+1#, as desired!

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