Prove that for every integer n ≥ 2.
P ( n + 1 , 2 ) − P ( n , 2 ) = 2 P ( n , 1 ) .
To prove:
For all integers n≥2, P(n+1,2)−P(n,2)=2P(n,1).
Given information:
P(n+1,2)−P(n,2)=2P(n,1)
Concept used:
P(n.r)=n!n−r!
Proof:
P(n+1,2)=( n+1)!( n+1−2)!=( n+1)!( n−1)!=( n+1)(n)( n−1)!( n−1)!=(n+1)n=n2+n
P
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