Prove that for every integer n ≥ 3 , P ( n + 1 , 3 ) − P ( n , 3 ) = 3 P ( n , 2 ) .
To prove:
P(n+1,3)−P(n,3)=3P(n,2)
Given information:
P(n+1,3)P(n,3)3P(n,2)
Concept used:
P(n.r)=n!n−r!
Calculation:
P(n+1,3)=( n+1)!( n+1−3)!=( n+1)!( n−2)!=( n+1)(n)( n−1)( n−2)!( n−2)!=(n+1)(n)(n−1)=n(n2−1)=n3−n
P(n,3)=n!( n−3)!=n( n−1)( n−2)( n−3)!( n−3)!
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