title: How To Solve Recurrence Relation with a quadratic term
body: <p>I'm trying to solve this recurrence relation. Here's what I've attempted so far, but I think I'm wrong. I would really appreciate some guidance.</p>
  
  <p>This is the recurrence relation I am trying to solve:- <strong>2T(n^1/2) + C</strong></p>
  
  <pre><code>T(n) = 2T(n^1/2) + C
  2((2T(n^1/4)+C) + C
  &gt;&gt; 4T(n^1/16) + 3C
  &gt;&gt; 8T(n^1/256) + 6C
  </code></pre>
  
  <p>So I can formulate it into this algebraic expression:-</p>
  
  <pre><code> (2^k)T(n^(1/2^k)) + 2k
  </code></pre>
  
  <p>So to solve the recurrence relation, I simply say</p>
  
  <pre><code>n^(1/(2^k)) = 1
  Therefore:-   2k = log (base n) 1
  But this makes k = 0....
  </code></pre>
  
  <p>I don't think this is correct. Please advise me, I'd be delighted to get some assistance!</p>