If n is not a positive integer or zero, the binomial expansion of (1+y)n yields, for−1
Use this generalized definition of binomial coefficients (which agrees with the one on page 12 for positive integral values of n) to evaluate
(b) √5 writing √5 = 2(1 + 1/4)1/2 and using the first four terms of the binomial expansion of (1+ 1/4)1/2.
Answer to relevant QuestionsWith reference to the generalized definition of binomial coefficients in Exercise 1.19, show that (a) (b) The pro at a golf course stocks two identical sets of women’s clubs, reordering at the end of each day (for delivery early the next morning) if and only if he has sold them both. Construct a tree diagram to show that if he ...In Example 1.4 we showed that a true–false test consisting of 20 questions can be marked in 1,048,576 different ways. In how many ways can each question be marked true or false so that (a) 7 are right and 13 are wrong; (b) ...Use Venn diagrams to verify that (a) (A ∪ B). C is the same event as A ∪ (B ∪ C); (b) A ∩(B ∪ C) is the same event as (A ∩ B) ∪ (A ∩ C); (c) A ∪ (B ∩ C) is the same event as (A ∪ B) ∩ (A ∪ C). An explosion at a construction site could have occurred as the result of static electricity, malfunctioning of equipment, carelessness, or sabotage. Interviews with construction engineers analyzing the risks involved led to ...
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