ISI2016-DCG-14

Question

For natural numbers $n,$ the inequality $2^{n}>2n+1$ is valid when

• A. $n\geq 3$
• B. $n<3$
• C. $n=3$
• D. None of these

Comments

https://gateoverflow.in/321210/isi2015-dcg-14

same question

Answer 1

We know that $2^n$ would always be greater than $2*n$(exponential increase > linear increase) after a certain point.

We just need to find that point.

The intersection point would occur when

$2^n = 2n+1$

On solving this we get $n \approx 2.6$.

Now after this i.e. after $n=2.6$ the inequality would hold for all values of $n$

$\therefore$ Option $A.$ is correct answer.