Question-70

Question-70

Prove that 3ⁿ < n! if n is an integer greater than 6.

The basis step is n = ?. The basis step is true since ?  <  ? .

Assume the statement foe n = k . Then

3^{k + 1} = 3.?   <  ?  =  ? ,

the  statement for n = ?.

 

Solution

n = 7.

Then basis step is true sincs 2187 < 5040.

3^k+1 =   < k+1.k! = k+1!,

n = k + 1.