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Alternating Pascal (Posted on 2011-12-08) Difficulty: 2 of 5
Prove that for any row of Pascal's Triangle if you alternately subtract and add terms you always get 0.

Note: this is obvious for odd rows [1-3+3-1=0]
but not so obvious for even rows [1-4+6-4+1=0]

  Submitted by Jer    
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Solution: (Hide)
This property will hold for any list of numbers formed in the way Pascal's Triangle is.

Each number from the previous row is used twice, one as part of a number with a + and once as part of a number with a -. This ensures they will all cancel out.

In fact, the numbers with a + will always have the same sum as the previous row and the - will be the opposite.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some Thoughtsre: Also true for pascal-like tables(spoiler)Ady TZIDON2011-12-09 10:03:53
SolutionAlso true for pascal-like tables(spoiler)Steve Herman2011-12-08 13:19:26
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