a garage floor measures 150 feet by 120 feet a scale drawing of the floor on grid paper uses a scale of 1 unit : 15feet what are
2 answers:
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We start by proving the statement is true for . In this case, the left hand side is simply:
The right hand side is:
So the property holds for .
Now we assume the property is valid for some and prove that it implies that it is also valid for
. That means we shall obtain:
We start by writing the property for and recognize that we've only added an extra term:
We now expand the square and merge everything together in a single fraction:
Since the desired expression has a facto, we may now divide the numerator by
, using, for instance, Ruffini's rule, in order to find it:
So we get:
We now add and subtract and
in order to obtain the form corresponding to
, since we know that it must appear:
So we finally got:
which is the desired result. So we proved that the statement is true for every integer .