Write the sum $in$ sigma notation.

$,\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+\frac{4}{5}+$cdots$+\frac{19}{20}$

${\displaystyle \underset{i=1}{\overset{20}{}}}\frac{i}{i+1}$

${\displaystyle \underset{i=1}{\overset{18}{}}}\frac{i}{i+1}$

${\displaystyle \underset{i=1}{\overset{19}{}}}\frac{i+1}{i}$

${\displaystyle \underset{i=1}{\overset{19}{}}}\frac{i}{i+2}$

${\displaystyle \underset{i=1}{\overset{19}{}}}\frac{i}{i+1}$

${\displaystyle \underset{i=1}{\overset{19}{}}}\frac{i}{i+2}$