Multiples of Pi/4
Pro Problems > Math > Logic > Proofs > Proof by InductionMultiples of Pi/4
Prove by induction that for any non-negative integer n,
tan ((4n + 1)p
4
Additional Question: Could this induction be extended to all integers, not just negative ones? If so, how?
Note: Without rigorous proof, we can see that this is true, since the angles which match the equation are all in the first and third quadrant, and all have reference triangles ofp
4
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Problem by BogusBoy
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Sum of Integers Proof
1 = 1 =
1 + 2 = 3 =
1 + 2 + 3 = 6 =
1 + 2 + 3 + 4 = 10 =
1 + 2 + 3 + 4 + 5 = 15 =
It appears from this that the sum of the first n positive integers is . Can you prove this by induction?
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1 + 2 + 3 + 4 = 10 =
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