Since by the principle of mathematical induction if p( n ) is true for n = 3 then that will be the minimum point to be considered for the process.Also that P ( n ) ⇒P(n+1)

when n = 1 the value is 64. By induction process the consecutive replacement of n = 2,3,4....will be multiples of 64.

Since when n = 1 , we get the inequality as 1>1, which is not true. also for n = 2 , we get 2>2, which is false. Hence the given statement is true for n>2

Since if n = 1 we have 3>4, which is not true . If n = 2 then 9>8, which is true.

when n = 1 , , which is not true.When n = 2, , which is false as well. Also when n = 3 we get .When n = 4 , Hence it is trure frm n = 4 .

When n = 1 we get , and when n = 2 we get ,. when n = 3 , which are inavlid inequations. Only when n = 4 we get , which is valid.

When n = 1 we have a + b.And the subsequent substitution of n as 2,3,... will result in the expression whose factor is a + b.

For each n N , n (n + 1 ) ( 2n + 1 ) is divisible by :

When n = 1 the value is 6 . The subsequent substitution will give the value as a multiple of 6.

When n = 1 we have 391 which is divisible by 17.

When n = 1 the value is 7.