# Math Help - Find sum of the following series?

1. ## Find sum of the following series?

Find sum of the following:

${n\choose 0} + \left({1\choose 1}{n\choose 1} + {2\choose 0}{n\choose 2}\right) + \left({2\choose 2}{n\choose 2} + {3\choose 1}{n\choose 3} + {4\choose 0}{n\choose 4}\right)$ $+\ \left({3\choose 3}{n\choose 3} + {4\choose 2}{n\choose 4} + {5\choose 1}{n\choose 5} + {6\choose 0}{n\choose 6}\right)$
$+\ \left({4\choose 4}{n\choose 4} + {5\choose 3}{n\choose 5} + {6\choose 2}{n\choose 6} + {7\choose 1}{n\choose 7} + {8\choose 0}{n\choose 8}\right)$ $+\ ...\ + {n\choose n}{n\choose n}$