\(B=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...+\frac{1}{20}\left(1+2+3+...+20\right)\)

\(=1+\frac{1}{2}.\frac{2\left(2+1\right)}{2}+\frac{1}{3}.\frac{3\left(3+1\right)}{2}+...+\frac{1}{20}.\frac{20\left(20+1\right)}{2}\)

\(=\frac{2}{2}+\frac{2+1}{2}+\frac{3+1}{2}+...+\frac{20+1}{2}\)

\(=\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+...+\frac{20}{2}\)

\(=\frac{2+3+4+...+20}{2}=\frac{\frac{20\left(20+1\right)}{2}-1}{2}=\frac{209}{2}\)

Đinh Đức Hùng trả lời sai rồi

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

B = 1+[1/2 (1+2) 2]/2 +[1/3 (1+2+3) 3]/2 +....+ [1/16 (1+2+3+...+20) 16] /2

B = 1+3/2 + 4/2 +...+ 17/2

B = 1/2 (2+3+4+....+17)

B= 1/2 [(2+7)16]/2

B= 76

Nhớ k cho mình nhé :D