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VOL. 77, NO. 5, DECEMBER 2004

Proof Without Words: A Triangular Identity 2 + 3 + 4 = 9 = 32 − 02 5 + 6 + 7 + 8 + 9 = 35 = 62 − 12 10 + 11 + 12 + 13 + 14 + 15 + 16 = 91 = 102 − 32 .. . 2 2 − tn−1 tn = 1 + 2 + · · · + n ⇒ t(n+1)2 − tn 2 = tn+1

n 2 +1 tn −1

n 2n + 1 = ( n + 1) + n = tn+1 − tn−1

tn

tn + 1

(n + 1)

2

tn +1 − t n −1

tn + 1

tntn−1 −1

tn +1 − tn −1

—–ROGER B. N ELSEN L EWIS & C LARK C OLLEGE P ORTLAND OR 97219

Proof Without Words: A Triangular Identity

Proof Without Words: A Triangular Identity. 2 + 3 + 4 = 9 = 32 − 02. 5 + 6 + 7 + 8 + 9 = 35 = 62 − 12. 10 + 11 + 12 + 13 + 14 + 15 + 16 = 91 = 102 − 32 ... tn = 1 + 2 ...
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