A machine made 3 1/2 pencils in 1/6 of a minute. It made pencils at a rate of how many per minute?
1 answer:
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Let
In order to prove this by induction, we first need to prove the base case, i.e. prove that P(1) is true:
So, the base case is ok. Now, we need to assume and prove
.
states that
Since we're assuming , we can substitute the sum of the first n terms with their expression:
Which terminates the proof, since we showed that
as required