1/ Cho S= \(\dfrac{1}{11} + \dfrac{1}{12} + \dfrac{1}{13} + ... + \dfrac{1}{19} + \dfrac{1}{20}\)
So sánh S với \(\dfrac{1}{2}\)
2/ Tìm x biết: \(\dfrac{x}{12}= \dfrac{-1}{24}- \dfrac{1}{8}\)
3/Tính 1 cách hợp lí: \(\dfrac{2}{5.7}+ \dfrac{2}{7.9}+ ...+ \dfrac{2}{19.21}\)
GIÚP MK VS!!! MK ĐG GẤP LẮM >.< MƠN M.N NHÌU Ạ!
. Ta có :
\(\dfrac{1}{11}>\dfrac{1}{20}\)
\(\dfrac{1}{12}>\dfrac{1}{20}\)
.................
\(\dfrac{1}{19}>\dfrac{1}{20}\)
\(\dfrac{1}{20}=\dfrac{1}{20}\)
\(\Leftrightarrow\dfrac{1}{11}+\dfrac{1}{12}+......+\dfrac{1}{20}>\dfrac{1}{20}+\dfrac{1}{20}+.....+\dfrac{1}{20}\)
\(\Leftrightarrow S>\dfrac{1}{20}.10\)
\(\Leftrightarrow S>\dfrac{1}{2}\)
2. \(\dfrac{x}{12}=\dfrac{-1}{24}-\dfrac{1}{8}\)
\(\Leftrightarrow\dfrac{x}{12}=-\dfrac{1}{6}\)
\(\Leftrightarrow6x=-12\)
\(\Leftrightarrow x=-2\)
Vậy ...
3. \(\dfrac{2}{5.7}+\dfrac{2}{7.9}+........+\dfrac{2}{19.21}\)
\(=\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+......+\dfrac{1}{19}-\dfrac{1}{21}\)
\(=\dfrac{1}{5}-\dfrac{1}{21}\)
\(=\dfrac{16}{105}\)
