Question

1/30 + 1/42 + 1/56 +.......1/32

Answer 1

Sửa đề thành \(\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+...+\dfrac{1}{132}\)

\(=\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+...+\dfrac{1}{11.12}\)

\(=\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+...+\dfrac{1}{11}-\dfrac{1}{12}\)

\(=\dfrac{1}{5}-\dfrac{1}{12}=\dfrac{7}{60}\)

Answer 2

\(\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+....+\dfrac{1}{132}\)

\(=\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+.....+\dfrac{1}{11}-\dfrac{1}{12}\)

\(=\dfrac{1}{5}-\dfrac{1}{12}=\dfrac{12}{60}-\dfrac{5}{60}=\dfrac{7}{60}\)

Answer 3

= 1/5x6 + 1/6 x7 + 1/7x8 + ..... 1/8x4

= 1/5 - 1/6+1/6 - 1/7 + 1/7 - 1/8 +.... + 1/8 - 1/4

= 1/5 - 1/4

= -1/20