How does this happen???? O 12:15PM
page 95
Solution:
P(n): n (n + 1) (n + 5), which is a multiple of 3.
It can be noted that P(n) is true for n = 1 since 1 (1 + 1)
1 + 5) = 12, which is a multiple of 3.
Let P(k) be true for some positive integer k, i.e.,
k (k + 1) (k + 5) is a multiple of 3.
.•.k (k + 1) (k + 5) = 3m, where m EN (1)
We shall now prove that P(k + 1) is true whenever P(k)
is true.
Consider
(k+5)+11
= 3m + (k + +10 + k +2}
= +(k+ =3xq, whew q = is some natural number
Therefore, (k is a multiple of 3.
Thus, P(k + 1) is true whenever P(k) is true.
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