Prove that if `rlt=slt=n ,t h e n^n P_s` is divisible by `^n P_r` .

Prove that if r<=s<=n, then ^(n)P_(s) is divisible by ^(n)P_(r).

Prove that quad if r<=s<=n then ^(^^)n_(P_(s)) is divisible by ^(^^)n_(P_(r))

If r le s le n , then prove that .^(n)P_(s) is divisible by .^(n)P_(r) .

If r lt s le n " then prove that " ^(n)P_(s) " is divisible by "^(n)P_(r).

If r lt s le n " then prove that " ^(n)P_(s) " is divisible by "^(n)P_(r).

If r lt s le n " then prove that " ^(n)P_(s) " is divisible by "^(n)P_(r).

Prove that P(n,n) = P(n,n-1)

Prove that : P(n,n)= 2P (n,n -2)

If P(n) is the statement “sum of first n natural numbers is divisible by n + 1", prove that P(r + 1) is true if P(r) is true.