Geometric Sum Proof
Pro Problems > Math > Logic > Proofs > Proof by InductionGeometric Sum Proof
Give a proof by induction to show that for every non-negative integer n:
20 + 21 + 22 + ... + 2n = 2n + 1 - 1
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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?
1(1 + 1)
2
1 + 2 = 3 =
2(2 + 1)
2
1 + 2 + 3 = 6 =
3(3 + 1)
2
1 + 2 + 3 + 4 = 10 =
4(4 + 1)
2
1 + 2 + 3 + 4 + 5 = 15 =
5(5 + 1)
2
n(n + 1)
2
Series Proof
Use a proof by induction to prove that the first n terms of the series
1
2
1
4
1
8
1
2n
2n - 1
2n
Square Sum Proof
Prove by induction that the sum of the first n positive perfect squares is:
n(n + 1)(2n + 1)
6
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