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Unformatted text preview: ssume
13 + 23 + 33 + · · · + k 3 = k (k + 1)
2 2 . 3. Induction Step. Prove (1) is true for n = k + 1. So we must prove
(k + 1) (k + 2)
2 3 13 + 23 + 33 + · · · + k 3 + (k + 1) =
So
LHS =
= 13 + 23 + 33 + · · · + k 3 + (k + 1)3
k (k + 1)
2 = (k + 1)2
2 = (k + 1) 2 = (k + 1) 2
3 + (k + 1)
k
2 2 + (k + 1) k2
+k+1
4
k 2 + 4k + 4
4
2 2 = (k + 1) (k + 2)
4 (k + 1) (k + 2)
2
= RHS.
= QED 2 2 . 2) Woman in front of a line of n people. Man in back of this line. Prove that
somewhere in the line t...
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This note was uploaded on 01/31/2014 for the course MATH 187 taught by Professor Holmes during the Fall '08 term at Boise State.
 Fall '08
 HOLMES
 Math, Integers

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