Suppose that the <span class="katex-r" data-latex="displaystyle n"></span>-th ∂ sum of a sies <span class="katex-r" data-latex="displaystyle sum_{n=1}^{∞} a_n"></span> is <span class="katex-r" data-latex="displaystyle S_n = ac{n-1}{n+1}"></span>, f a <span class="katex-r" data-latex="displaystyle n ≥ 1"></span>. F∈d <span class="katex-r" data-latex="displaystyle a_{n+1}"></span>, <span class="katex-r" data-latex="displaystyle n ≥ 1"></span>, and the sum of the sies <span class="katex-r" data-latex="displaystyle sum_{n=1}^{∞} a