Let P(n) be the statement:
"`n^(3)+n` is divisible by 3."
i. Prove that P(3) is true.
ii. Verify whether the statement is true for n = 4.

If ninN" then "n^(3)+2n is divisible by

Prove that 3^(2n)-1 is divisible by 8.

Consider the statement " 7^(n)-3^(n) is divisible by 4" i. Verify the result for n = 2. ii. Prove the statement using mathematical induction.

Let P(n) denote the statement that n^(2)+n is odd. It is seen that P(n) = P(n + 1). P(n) is true for all.

Using the words ''necessary and sufficient'' rewrite the statement ''The integer n is odd if and only if n^(2) is odd''. Also check whether the statement is true.

Prove that if rlt=slt=n ,t h e n ' n P_s is divisible by n P_r .

In an n-type silicon , which of the following statements is true ?

Prove that 2.7^(n)+ 3.5^(n)-5 is divisible by 24 for all n in N