Question

 a, tính tổng 

1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/110 + 1/132

b, tính nhanh 

( 3/29 - 1/5 ). 29/3

 

Answer 1

\(\frac{1}{20}+\frac{1}{30}+...+\frac{1}{132}\)

\(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{11.12}\)

\(=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{12}\)

\(=\frac{1}{4}-\frac{1}{12}=\frac{3-1}{12}=\frac{2}{12}=\frac{1}{6}\)

Answer 2

\(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{110}+\frac{1}{132}\)
\(\frac{1}{4\times5}+\frac{1}{5\times6}+\frac{1}{6\times7}+\frac{1}{7\times8}+\frac{1}{8\times9}+...+\frac{1}{11\times12}\)
\(=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}+...+\frac{1}{11}-\frac{1}{12}\)
\(=\frac{1}{4}-\frac{1}{12}=\frac{3-1}{12}\)
\(=\frac{2}{12}=\frac{1}{6}\)