Saturday, January 27, 2018

College Algebra, Chapter 9, 9.6, Section 9.6, Problem 24

Evaluate the expression
(50)(51)+(52)(53)+(54)(55)

Recall that the binomial coefficient is denoted by (nr) and is defined by
Notice that these are precisely the entries in the fifth row of Pascal's Triangle.

(50)=5!0!(50)!=1(51)=5!1!(51)!=5(52)=5!2!(52)!=10(53)=5!3!(53)!=10(54)=5!4!(54)!=5(55)=5!5!(55)!=1

Thus,

(50)(51)+(52)(53)+(54)(55)=15+1010+51=0

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