\(B=1+\dfrac{1}{2}\left(1+2\right)+\dfrac{1}{3}\left(1+2+3\right)+...+\dfrac{1}{20}\left(1+2+...+20\right)\)
\(B=1+\dfrac{1}{2}.2.3:2+\dfrac{1}{3}.3.4:2+...+\dfrac{1}{20}.20.21:2\)
\(B=\dfrac{2}{2}+\dfrac{3}{2}+...+\dfrac{21}{2}\)
\(B=\dfrac{2+3+...+21}{2}\)
\(B=\dfrac{230}{2}\)
\(\Rightarrow B=115\)