title: Finding the sum of Fibonacci Numbers
body: <p>What would be the most efficient way to calculate the sum of Fibonacci numbers from <code>F(n)</code> to <code>F(m)</code> where <code>F(n)</code> and <code>F(m)</code> are nth and mth Fibonacci numbers respectively and 0 =&lt; n &lt;= m &lt;10<sup>9</sup> (with F(0)=0, F(1)=1).</p>
  
  <p>For example, if <code>n=0</code>, <code>m=3</code>, we need to find <code>F(0)+F(1)+F(2)+F(3)</code>.</p>
  
  <p>Just by brute force it will take long time for the range of <code>n</code> and <code>m</code> mentioned. If it can be done via matrix exponentiation then how?</p>