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.
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
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