A wooden block measures 2 inches by 2 inches by 3 inches. A wedge is cut off from each corner of the block by slicing at points
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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
so we have a 33, namely two real solutions for that quadratic.
usually that number goes into a √, if you have covered the quadratic formula, you'd see it there, namely that'd be equivalent to √(33), now 33 is a prime number, and √(33) is yields an irrational value, specifically because a prime number is indivisible other than by itself or 1.
so 33 can only afford us two real irrational roots.