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\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{200.201}\)
=\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{200}-\frac{1}{201}\)
=\(\frac{1}{2}-\frac{1}{201}\)
=\(\frac{199}{402}\)
\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{200.201}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{200}-\frac{1}{201}\)
\(=\frac{1}{2}-\frac{1}{201}=\frac{199}{402}\)
\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{19.20}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{20}\)
\(=\frac{1}{2}-\frac{1}{20}\)
\(=\frac{9}{20}\)
Ta có công thức :\(\frac{1}{n\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}\)
\(\Rightarrow\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{19.20}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{19}-\frac{1}{20}\)
\(=\frac{1}{2}-\frac{1}{20}\)
\(=\frac{9}{20}\)
Lời giải:
$=(0,25\times 0,04)\times 3,6+ 360+3,6\times 8$
$=0,01\times 3,6+360+28,8$
$=0,036+360+28,8=388,836$
Ta có : \(\frac{1}{3.4}+\frac{1}{4.5}+......+\frac{1}{89.90}\)
\(=\frac{1}{3}+\frac{1}{4}-\frac{1}{4}+.......+\frac{1}{89}-\frac{1}{90}\)
\(=\frac{1}{3}-\frac{1}{90}=\frac{30}{90}-\frac{1}{90}=\frac{29}{90}\)
\(\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{89.90}\)
\(=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{89}-\frac{1}{90}\)
\(=\frac{1}{3}-\frac{1}{90}\)
\(=\frac{29}{90}\)
\(4,5\times3,6-40,5+6,4\times4,5-6,5\)
\(=\left(4,5\times3,6+6,4\times4,5\right)-\left(40,5+6,5\right)\)
\(=4,5\times\left(3,6+6,4\right)-47=4,5\times10-47=45-47=-2\)