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 + 1 for n in Pn.

.

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 .


Mathematics

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