1 / 7

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

palani
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related