Prove via induction the following properties of Pascal’s
Triangle:
•P(n,2)=(n(n-1))/2
• P(n+m+1,n) = P(n+m,n)+P(n+m−1,n−1)+P(n+m−2,n−2)+···+P(m,0) for
all...
Prove via induction the following properties of Pascal’s
Triangle:
•P(n,2)=(n(n-1))/2
• P(n+m+1,n) = P(n+m,n)+P(n+m−1,n−1)+P(n+m−2,n−2)+···+P(m,0) for
all m ≥ 0
Prove these scenarios by mathematical induction:
(1) Prove n2 < 2n for all integers
n>4
(2) Prove that a finite set with n elements has 2n
subsets
(3) Prove that every amount of postage of 12 cents or more can
be formed using just 4-cent and 5-cent stamps
Prove by induction on n that the number of distinct handshakes
between n ≥ 2 people in a room is n*(n − 1)/2 .
Remember to state the inductive hypothesis!