If `|A|=n,` then prove that `|P(A)|=2^(n)`

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

If the first and the nth term of a G.P. are a and b, respectively, and if P is the product of n terms , prove that P^(2)=(ab)^(n) .

if S is the sum,P the product and R the sum of reciprocals of n terms in G.P. prove that P^(2)R^(n)=S^(n)

If the first and the nth terms of a G.P,are a and b ,respectively,and if P is hte product of the first n terms prove that P^(2)=(ab)^(n).

If S_(m)=m^(2) p and S_(n)=n^(2)p , where m ne n in an AP then prove that S_(p) =P^(3)

Prove that 2^(n)>n,n in N

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

Prove that n!(n+2)=n!+(n+1)!

if P(n) be the statement 10n+3 is a prime number", then prove that P(1) and P(2) are true but P(3) is false.