Prove that for every positive integer n≥1,n2+nn \geq 1, n^2 + nn≥1,n2+ | Discrete Structures 2076

Discrete Structures20765 marksmathematical Induction

Prove that for every positive integer n≥1,n2+nn \geq 1, n^2 + nn≥1,n2+n is even integer using mathematical induction. [5]

An integer is even if it can be written in the form 2k for some integer k. Also note that: $n^2 + n = n(n+1)$ This is the product of two consecutive integers, which will be useful in each step. --- Substitute n = 1: $n^2 + n = (1)^2 + (1) = 1 + 1 = 2$ Since 2 = 2(1), which is of the form 2k, ...

An integer is even if it can be written in the form 2k for some integer k. Also note that: $$n^2 + n = n(n+1)$$ This is the product of two consecutive integers, which will be useful in each step. --- Substitute n = 1: $$n^2 + n = (1)^2 + (1) = 1 + 1 = 2$$ Since 2 = 2(1), which is of the form 2k, ...

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