BBS: Inland Empire Archive Date: 04-08-93 (18:11) Number: 362 From: MICHEL BERTLER Refer#: NONE To: EARL MONTGOMERY Recvd: NO Subj: Summial Conf: (2) Quik_Bas

EM> I was fooling around with writing a formula to figure the total EM> # of blocks required to build a pyramid as described below. EM> Notice each descending row has 1 more block than the level EM> above. I doNOThave a background in math! But I saw a EM> relationship and came up with this formula: EM> . EM> . . EM> . . . EM> . . . . EM> . . . . . EM> . . . . . . EM> . . . . . . . EM> . . . . . . . . EM> . . . . . . . . . EM> . . . . . . . . . . It's the `summial' where: ä = n(n+1)/2 In the above formula, `n' is the number of rows of dots from any summit of the triangle to its opposed side and `ä' (sigma) is the total number of dots. 10(10+1)/2 = 55 This could also be easily verified by long addition: 1+2+3+4+5+6+7+8+9+10 = 55 The same formula could also be written as: ä = (ný+n)/2 EM> Earl's Law <smile> EM> Total Blocks=Level * Level value EM> Level Level value EM> 1 1 EM> 2 1.5 EM> 3 2 EM> 4 2.5 EM> 5 3 EM> 6 3.5 EM> 7 4 EM> 8 4.5 EM> 9 5 EM> 10 5.5 EM> My question is: Is there a math rule similar to this? And if so EM> what is it called? By recurrent definition I would say: (L+1)/2 = Lv, where L stands for `Level' and Lv for `Level value' from `Earl's arithmetical suite'! Keep in mind that sommial & factorial are both arithmetical suites only dealing with integers! Michel --- GoldED * Origin: Blainville, Quebec (1:242/130)

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