title: ratio of running times when N doubled in big O notation
body: <p>I learned that,using Big O notation</p>
  
  <pre><code>O(f(n)) + O(g(n)) -&gt; O(max(f(n),g(n))
  
  O( f(n) )* O( g(n)) -&gt; O( f(n) g(n))
  </code></pre>
  
  <p>but now, I have this equation for running time T for input size N</p>
  
  <pre><code>T(N) = O(N^2)  // O of N square
  </code></pre>
  
  <p>I need to find the ratio <code>T(2N) / T(N)</code></p>
  
  <p>I tried this</p>
  
  <pre><code>T(2N) / T(N) --&gt; O((2N)^2) /O( N^2)  --&gt; 4
  </code></pre>
  
  <p>Is this correct? Or is the above division invalid?</p>