Question

prove that which are number will be always be number
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Answer 1

Step-by-step explanation:

You can also prove it through induction, although the odd times even answers are more quick and obvious.

Test for n = 1: well, this gives us 1 * 2, which is certainly divisible by 2

Assume true for n = m: this means that m*(m+1) is assumed to be divisible by 2 and equal to 2k, where k is some integer.

Test for n = m+1:

(m+1)(m+2) = m(m+1) + m + m + 2 (expand out both sides to check this)

this becomes:

m(m + 1) + 2m + 2 = m(m+1) + 2(m+1) = 2k + 2(m + 1)

This is obviously divisible by 2.

Therefore, n(n + 1) is always divisible by 2, if n a positive integer.