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Đặt biểu thức là A, ta có:
\(A=1+\frac{1}{2}.\left(1+2\right)+\frac{1}{3}.\left(1+2+3\right)+...+\frac{1}{20}.\left(1+2+3+...+20\right)\)
\(A=1+\frac{1}{2}.2.3:2+\frac{1}{3}.3.4:2+...+\frac{1}{20}.20.21:2=\frac{2}{2}+\frac{3}{2}+...+\frac{21}{2}\)
\(A=\frac{2+3+4+...+21}{2}=\frac{230}{2}=115\)
a, \(\frac{x}{5}=\frac{2}{3}\Leftrightarrow x=\frac{10}{3}\)
b, \(\frac{x}{-24}=\frac{20}{42}\Leftrightarrow x=-\frac{80}{7}\)
c, \(\frac{x+3}{15}=\frac{1}{3}\Leftrightarrow3x+9=15\Leftrightarrow x=2\)
d, \(\frac{2}{3}x-\frac{3}{2}x=\frac{5}{12}\Leftrightarrow x\left(\frac{2}{3}-\frac{3}{2}\right)=\frac{5}{12}\Leftrightarrow-\frac{5}{6}x=\frac{5}{12}\Leftrightarrow x=-\frac{1}{2}\)
a) \(x+\frac{-7}{15}=-1\frac{1}{20}\)
\(x=\frac{-21}{20}\)\(+\frac{7}{15}\)
\(x=\frac{-7}{12}\)
b) \(\left(3\frac{1}{2}-x\right)\cdot1\frac{1}{4}=-1\frac{1}{20}\)
\(\left(\frac{7}{2}-x\right)\cdot\frac{5}{4}=-\frac{21}{20}\)
\(\frac{7}{2}-x=\frac{-21}{20}\cdot\frac{4}{5}\)
\(\frac{7}{2}-x=\frac{-21}{25}\)
\(x=\frac{7}{2}+\frac{21}{25}\)
\(x=\frac{217}{50}\)
Hc tốt #
Ta có
1+1/2(1+2)+....+1/20(1+2+3+...+20)
= 2/2+3/2+.....+19/2
=(2+3+....+19)/2
= 189/2