Prove the formula for all natural numbers n.
?
?
List the steps involved.
What will be an ideal response?
?Step 1: We must verify that
is true. However,
is just the statement that
, which is true.
Step 2: Assuming that is true, we must prove that
is true. Let's examine
and
.
.
is obtained by substituting k + 1 for n in
.
.
If we add to the both sides of the equation for
, we'll get the equation for
.
Since equation for follows from equation for
, we have demonstrated that
.
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Mathematics