Compute the following sum:12 · 3 + 13 · 4 + · · · + 1(n + 1)(n + 2).Prove that your answer is true for all n ∈ N using induction.

The problem seems to be a bit unclear, but I'll try to interpret it as best as I can. It seems like you're asking for the sum of a series that looks something like this:

12 * 3 + 13 * 4 + 14 * 5 + ... + 1(n + 1)(n + 2)

This looks like an arithmetic series where the nth term can be represented as 1(n + 1)(n + 2).

To find the sum of an arithmetic series, we can use the formula:

Sum = n/2 * (a + l)

where n is the number of terms, a is the first term, and l is the last term.

However, in this case, the series doesn't seem to be arithmetic because the difference between the terms is not constant.

If the series is indeed as I interpreted, then it's not an arithmetic series and