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Sum of Integers Proof

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

Sum of Integers Proof

1  = 1 =
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

It appears from this that the sum of the first n positive integers is
n(n + 1)
2
. Can you prove this by induction?

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Problem by BogusBoy

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