14.
\(\lim\dfrac{\left(2n^3+1\right)^4\left(2n+3\right)^{10}}{2n^{22}+2}=\lim\dfrac{\left(2+\dfrac{1}{n^3}\right)^4\left(2+\dfrac{3}{n}\right)^{10}}{2+\dfrac{2}{n^{22}}}\)
\(=\dfrac{2^4.2^{10}}{2}=2^{13}\)
15.
\(d=\dfrac{u_{11}-u_1}{11-1}=-2\)
\(\Rightarrow n=\dfrac{u_n-u_1}{d}+1=\dfrac{16-50}{-2}+1=18\)
16.
\(\Leftrightarrow\overrightarrow{GS}+\overrightarrow{GO}+\overrightarrow{OA}+\overrightarrow{GO}+\overrightarrow{OB}+\overrightarrow{GO}+\overrightarrow{OC}+\overrightarrow{GO}+\overrightarrow{OD}=\overrightarrow{0}\)
\(\Leftrightarrow\overrightarrow{GS}+4\overrightarrow{GO}=\overrightarrow{0}\)
\(\Leftrightarrow\overrightarrow{GS}=4\overrightarrow{OG}\)
