# Sum of Integers Proof

Pro Problems > Math > Logic > Proofs > Proof by Induction## 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

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Problem by BogusBoy

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