Use the principle of mathematical induction to show that the

Use the principle of mathematical induction to show that the statement is true for all n 6

(n+1)² 2ⁿ

^Thanks!

Solution

(n+1)^2 <= 2^n

for n>=6

for n = 6 ; (6+1)^2 <= 64 ----> 49 <=64

Let us assume it holds true for n = k ; (k+1)^2 <= 2^k

Now for n =k+1 ; (k +2)^2 < = 2^(k+1)

(k+1 +1)^2<= 2^(k+1)

As it holds true for n=k , it also holds true for n = k+1

Hence Proved