title: How to prove binomial coefficient is asymptotic big theta of two to the power n?
body: <p>I am stuck at this problem. I think it is equivalent to show 2m choose m is big theta of 4 to the power n, but still find difficult to prove it.</p>
  
  <p><a href="https://i.stack.imgur.com/l7ie6.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/l7ie6.jpg" alt="enter image description here"></a></p>
  
  <p>Thanks of @LutzL's suggestion. I thought of stirling's approximation before. <a href="https://i.stack.imgur.com/U1iuP.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/U1iuP.jpg" alt="enter image description here"></a></p>