Using principle of mathematical induction, prove the following `1+3+5+...+(2n - 1)=n^2`

Using principle of mathematical induction, prove that: 1+3+5+………..+(2n-1)= n^2 .

By using the principle of mathematical induction , prove the follwing : P(n) + 1+3+5+……….+(2n-1) = n^2 , n in N

Using the principle of mathematical induction, prove each of the following for all n in N 1+2+3+4+…+N=1/2 N(N+1) .

By using the Principle of Mathematical Induction, prove the following for all n in N : 1.1! +2.2! +3.3! +.......+ n.n! = (n+1)!-1 .

Using principle of mathematical induction, prove that 1 + 3 + 3^(2) + … 3^(n-1) = (3^(n) - 1)/(2)

Using principle of mathematical induction, prove that for all n in N, n(n+1)(n+5) is a multiple of 3.

Using principle of mathematical induction, prove that for all n in N, n(n+1)(n+5) is a multiple of 3.

Using principle of mathematical induction, prove that for all n in N, n(n+1)(n+5) is a multiple of 3.

By the Principle of Mathematical Induction, prove the following for all n in N : 5^(2n)-1 is divisible by 24.

By the Principle of Mathematical Induction, prove the following for all n in N : 5+15+45+.....+5 (3)^(n-1) = 5/2 (3^n-1) .