Prove that product of two consecutive integer is an even integer

Asked by dharmindersandhu1979 | 17th Apr, 2019, 01:43: PM

Expert Answer:

let space straight n space and space straight n plus 1 space be space the space two space integers
straight n open parentheses straight n plus 1 close parentheses
now space two space cases space are space possible

Case space 1
straight n equals space even space number space equals space 2 straight k
product equals 2 straight k open parentheses 2 straight k plus 1 close parentheses equals 4 straight k squared plus 2 straight k equals 2 open parentheses 2 straight k squared plus straight k close parentheses... even

Case space 2
straight n equals space odd space number space equals space 2 straight k plus 1
product equals open parentheses 2 straight k plus 1 close parentheses open parentheses 2 straight k plus 2 close parentheses equals 4 straight k squared plus 6 straight k plus 2 equals 2 open parentheses 2 straight k squared plus 3 straight k plus 1 close parentheses... even
 
So we get even numbers in both cases

Answered by Arun | 18th Apr, 2019, 09:47: AM

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