prove that n3 + 3n2 + 5n + 3 is divisible by 3 for any natural number n
prove that n3 + 3n2 + 5n + 3 is divisible by 3 for any natural number n
geeta , 11 Years ago
Grade 11
Algebra> prove that n 3 + 3n 2 + 5n + 3 is divisib...
2 AnswersArun Kumar
Hello Student,
n^3 + 3n^2 + 5n + 3
=n^3 + 3n^2 + 2n+3n + 3
=n(n^2 + 3n + 2)+3n + 3
=n(n+1)(n+2)+3n+3
=n^3 + 3n^2 + 2n+3n + 3
=n(n^2 + 3n + 2)+3n + 3
=n(n+1)(n+2)+3n+3
Prooved
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty
mycroft holmes
By Fermat’s theorem, n3-n is divisible by 3.
Hence n3+3n2+5n+3 = (n3-n)+(3n2+6n+3) = 3m+3(n+1)2 for some integer m making the expression obviously a multiple of 3.
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