Pascal’s Triangle
M117, October 5, 2011 (due October 7, 2011)
Your name:
We can arrange the binomial coefficients nk into a triangle by letting n be the row number
and k be the column number. The result is called “Pascal’s Triangle”.
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(1) Rewrite Pascal’s triangle using the numbers instead of the symbols by replacing each
entry with its numerical value.
(2) Using the previous row, how are the numbers found for the next row? (Find the next
row using the last row given.)
(3) Find the triangular numbers in Pascal’s triangle. What is the explicit formula that
this gives for the nth triangular number? Why doesn’t this contradict the explicit
formula we found in class?
(4) Do you notice any symmetry in the triangle? (Explain.)
(5) What is the sum of the entries in the nth row? (Explain.)