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

By using the principle of mathematical induction , prove the follwing : P(n) : 2 + 4+ 6+ …..+ 2n =n(n+1) , n in N

By using the principle of mathematical induction , prove the follwing : P(n) : (2n + 7) lt (n+3)^2 , n in N

By using the principle of mathematical induction , prove the follwing : P(n) :( 1+x)^n gt=1 + nx, x gt (-1) , n in N

By using the principle of mathematical induction , prove the follwing : P(n) : 1/2 + 1/4 + 1/8 + ……..+ (1)/(2^n) = 1 - (1)/(2^n) , n in N

By using the principle of mathematical induction , prove the follwing : P(n) : 1^2 + 2^2 + 3^2+…………+n^2 = n/6 (n+1) (2n+1), n in N

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

By using the principle of mathematical induction , prove the follwing : P(n) : (1)/(1.2) + (1)/(2.3) + (1)/(3.4) + …….+ (1)/(n(n+1)) = (n)/(n+1) , n in N

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

By using the principle of mathematical induction , prove the follwing : (1)/(1.4) + (1)/(4.7) + (1)/(7.10) + ………..+ (1)/((3n - 2)(3n+1)) = (n)/(3n + 1) , n in N

Prove the following by using the principle of mathematical induction for all n in N 1^2 +3 ^2 + 5^2 +………..+ (2n-1)^2 = (n(2n - 1)(2n+1))/(3)