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Kenneth Rosen Edition 7 Exercise 6.4 Question 12 (Page No. 421)

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The row of Pascal’s triangle containing the binomial coefficients $\binom{10}{k},\: 0 \leq k \leq 10, \:\text{is:}\: 1\:\: 10\:\: 45\:\: 120\:\: 210\:\: 252\:\: 210\:\: 120\:\: 45\:\: 10\:\: 1$ Use Pascal’s identity to produce the row immediately following this row in Pascal’s triangle.
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Using Pascal’s identity C(n, k) + C(n, k + 1) = C(n + 1, k + 1) and the identities C(n, 0) = C(n, n) = 1,

we obtain the row C(11, 0) C(11, 1) . . . C(11, 7) C(11, 8) C(11, 9) C(11, 10) C(11, 11)

in the Pascal triangle from the given row: 1 11 55 165 330 462 462 330 165 55 11 1.

 

 

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Kenneth Rosen Edition 7 Exercise 6.4 Question 20 (Page No. 421)
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