The first six rows of Pascal's Triangle look like:

 SUM 1 n = 0 1 = 20 1 1 n = 1 2 = 21 1 2 1 n = 2 4 = 22 1 3 3 1 n = 3 8 = 23 1 4 6 4 1 n = 4 16 = 24 1 5 10 10 5 1 n = 5 32 = 25

There is an obvious pattern in this arrangement. Each row begins and ends with 1. The "middle" entries are obtained by adding the two numbers in the row above it between which it falls.

The row corresponding to n = 6 is

1  6  15  20  15  6 1

and the sum of the entries is 64 = 26.

Another interesting and useful feature is that the sum of the entries in each row is equal to 2n

REFERENCES

[1] Musser, Gary L. and William F. Burger, Mathematics for Elementary Teachers: A Contemporary Approach, Fourth Edition, Prentice-Hall, 1997.

[2] Rose, Israel H., A Modern Introduction to College Mathematics, John Wiley & Sons, Inc., 1959.
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}