Wirte the sum using sigma notation:
112+123+134++1215216=n=1AB\displaystyle {\frac{{{1}}}{{{1}\cdot{2}}}}+{\frac{{{1}}}{{{2}\cdot{3}}}}+{\frac{{{1}}}{{{3}\cdot{4}}}}+\cdots+{\frac{{{1}}}{{{215}\cdot{216}}}}={\sum_{{{n}={1}}}^{{{A}}}}{B}, where
A=\displaystyle {A}=   ,
B=\displaystyle {B}=   .