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What percentage of the numbers in Pascal’s Triangle are even?

What percentage of the numbers in Pascal’s Triangle are even?. 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1. Pascal’s Triangle E + O = O O + E = O E + E = E O + O = E. O O O O E O

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What percentage of the numbers in Pascal’s Triangle are even?

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  1. What percentage of the numbers in Pascal’s Triangle are even? 1 1 1 1 2 1 1 3 3 1 1 46 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1

  2. Pascal’s TriangleE +O = O O+ E =OE + E = E O + O= E O O O OEO O O O O OE E EO O OE E O O O E OE OEO O O O O O O O O

  3. Rows Proportion (evens) 8 9/36 = .250 16 55/136 = .404 32 285/528 = .539 64 1351/2080 = .650 128 6069/8256 = .735 256 26335/32896 = .801 512 111645/131328 = .850

  4. Rows Proportion (evens) 1,024 465751/524800 = .888 2,048 1921029/2098176 = .916 4,096 7859215/8390656 = .937 8,192 31964205/33558528 = .953 16,384 129442951/134225920 = .964 32,768 522538389/536887296 = .973 65,536 2104469695/2147516416 = .980

  5. Rows Proportion (evens) Based upon a geometric estimate 131,0728460859965/8590000128 = .985 262,144 33972448951/34359869440 = .989 524,288* = .991 1,048,576* = .994

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