Use mathematical induction to prove that the sum of the entires of the $k$-th row of Pascal’s Triangle is $2^k$. Begin by proving that the row sum for any particular row is double that for the previous row.
I am having a hard time trying to figure out how to prove that the row sum for any particular row is double that for the previous row. I know how to show for row one, row two and so forth but once I get to row n I know that the sum has to be row(n-1)(2), but I have no idea how to prove that. I know that each row's sum can be written as $2^k$ where $k$ is the row number. I was wondering if anyone can give me a hint or start me off.