Evaluating $\sum_{i=0}^{\log_2(7)} 2^i$. What am I doing wrong?
Solution 1:
$\displaystyle\sum_{i=0}^{\log_2(7)} 2^i$ is not mathematically correct.
When using the sigma notation, the indices are the elements of a finite set; not only natural numbers are allowed; you can sum on any finite set you want.
However, when we write $\displaystyle\sum_{i=0}^{p},$ we mean that $i\in\{0,1,2,\ldots,p\},$ where $p$ is a natural number.