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

Related Videos

This video explains the statement of Euclid's Division lemma and algorithm ...

Determination of H.C.F and L.C.M of numbers using Prime Factorization and ...

Discuss rational and irrational numbers and express them on the number lin...

This video explains the statement of Euclid's Division lemma and algorithm ...

Determination of H.C.F and L.C.M of numbers using Prime Factorization and s...

Ask Doubt

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.