I am trying to solve a problem with Constructive Induction. But I really don't understand what Constructive Induction is. Can anyone explain it to me using the following problem as an example? Thanks
Use constructive induction to derive a formula for the following:
Of course, that is not the complete proof.
The formula has been derived by examining a pattern from the first few terms of n.
To be sure whether this formula holds for all n natural numbers,
we try to establish that the formula being true for some n=k, causes the formula to be true for the next n=k+1.
Because we use n or k, we are attempting to establish this term-by-term relationship in general for all pairs of terms.
If it works then a chain-reaction is established for all n.
To do this we try to prove
Therefore, we start by adding the next cube
Therefore the formula holds for all n, as it holds for n=1.