Multiples of Pi/4Pro Problems > Math > Logic > Proofs > Proof by Induction
Multiples of Pi/4
Prove by induction that for any non-negative integer n,tan (
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 of
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Give a proof by induction to show that for every non-negative integer n:
20 + 21 + 22 + ... + 2n = 2n + 1 - 1
1 + 2 = 3 =
1 + 2 + 3 = 6 =
1 + 2 + 3 + 4 = 10 =
1 + 2 + 3 + 4 + 5 = 15 =
Prove by induction that the sum of the first n positive perfect squares is:
Prove by induction that for every integer n ≥ 1, 11n is one more than a multiple of ten.
Note: Proof by induction is not the simplest method of proof for this problem, so an alternate solution is provided as well.
Prove by induction that for all integers n>3:
3n > 9n
Use a proof by induction to prove that the first n terms of the series