Question

Mathematical INDUCTION​

Answer 1

Answer:

the answer in b) 7

Step-by-step explanation:

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Answer 2

Answer:

here is your solution

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Step-by-step explanation:

$so \: here \: \: for \: given \: expression \\ n ∈ N \\ \\ (n {}^{2} + 7n + 6)(n {}^{2} + 7n + 10)(n {}^{2} + 7n + 12) \\ \\ = [(n + 6)(n + 1)] \:[(n + 5)(n + 2)] \: [(n + 4)(n + 3)] \\ \\ = (n + 6)(n + 5)(n + 4)(n + 3)(n + 2)( n+ 1) \\ \\ = (n + 6) \: ! \\ \\ = 6n(n + 6) \: ! \\ \\ which \: is \: divisible \: \: and \: multiple \: \\ of \: 6 \\ \\ hence \: \: by \: principle \\ of \: mathematical \: \: induction \\ we \: can \: conclude \: that \\ \\ given \: expression \: \: is \: \: divisible \: \\ by \: \: 6 \: !$