Homework SourseUse the principle of mathematical induction to prove that 2n
Use the principle of mathematical induction to prove that 2|(n^2 + n) for all n greaterthanorequalto 0. (recall that the symbol \"|\" means \"divides\")![Use the principle of mathematical induction to prove that 2|(n^2 + n) for all n greaterthanorequalto 0. (recall that the symbol \](/WebImages/45/use-the-principle-of-mathematical-induction-to-prove-that-2n-1143442-1761613838-0.webp "Use the principle of mathematical induction to prove that 2|(n^2 + n) for all n greaterthanorequalto 0. (recall that the symbol \")
Solution
When n = 0, n2 +n = 0 so that 2| n2 +n. Further, when n =1, n2 +n = 2 so that 2| n2 +n. Also, when n =2, n2 +n = 6 so that 2| n2+n. When n = 3, n2 +n =12 so that 2| n2+n. Hence by induction, 2| n2 +n for all n 0.
