Prove the formula for all natural numbers n.
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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 .

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 is obtained by substituting + 1 for n in .

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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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