Explain the connections between Exercises 1, 2, and 3.
Exercise 1
Show that n+1Cr = nCr-1 + nCr.
Exercise 2
The array commonly called Pascal’s triangle can be defined by giving enough information to establish its pattern.
(a) Write the next three rows of Pascal’s triangle.
(b) Give a rule for building the next row from the previous row(s).
Exercise 3
Pascal’s triangle can also be defined by an explicit pattern. Use the results of Exercises 4 and 5 to give an explicit rule for building the nth row of Pascal’s triangle.
Exercise 4
(a) Find the number of subsets of each possible size for a set containing four elements.
(b) Find the number of subsets of each possible size for a set containing nelements.
Exercise 5
The array commonly called Pascal’s triangle can be defined by giving enough information to establish its pattern.
(a) Write the next three rows of Pascal’s triangle.
(b) Give a rule for building the next row from the previous row(s).
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