Show that the eξst two convgent sies <span class="katex-r" data-latex="displaystyle sum_{n=1}^{∞} a_n"></span> and <span class="katex-r" data-latex="displaystyle sum_{n=1}^{∞} b_n"></span> such that the ∏uct <span class="katex-r" data-latex="displaystyle sum_{n=1}^{∞} c_n = (sum_{n=1}^{∞} a_nright)(sum_{n=1}^{∞} b_nright)"></span> is divgent. He, c_n = sum