prove that 1+5+9+ . . .+(4n-3)=n(2n-1), for all natural number n.

1+5+9+...+(4n-3)=n(2n-1) for all natural numbers n

Prove that 1+2+2^(2)+ . . .+2^(n)=2^(n+1)-1 , for all natural number n.

Prove that 1+2+2^(2)+ . . .+2^(n)=2^(n+1)-1 , for all natural number n.

Prove each of the statements by the principle of mathematical induction : 1+5+9+……+(4n-3)= n(2n-1) for all natural numbers n .

prove that 3^(2n)-1 is divisible by 8, for all natural numbers n.

prove that 3^(2n)-1 is divisible by 8, for all natural numbers n.

Prove that : (2n) ! = 2^n (n!)[1.3.5.... (2n-1)] for all natural numbers n.

Prove 1 + 5 + 9 + ... + (4n - 3) = n(2n - 1), AA n in N

prove that 2+4+6+…2n=n^(2)+n , for all natural numbers n.

prove that 2+4+6+…2n=n^(2)+n , for all natural numbers n.