MathJax快速範本-雜級數推導計算

 $\Large 令 \sum_{k=1}^{8}[(2k+1)\cdot 2^{k}]=S$

  $$\begin{equation}\begin{split}  &S=3×2^1+&5×2^2+7×2^3+......+17×2^8 \\  2&S= & 3×2^2+5×2^3+......+15×2^8+17×2^9 \\ \hline \\ (2)-(1) &S=17×2^9-&2×[2^2+2^3+......+2^8]-3×2^1 \\ &S=17×2^9-&2×(2^9-2^2)-6 \\ &S=15×2^9+&2 \end{split}\end{equation}$$