\(A=\dfrac{18}{2.5}+\dfrac{18}{5.8}+...+\dfrac{18}{203.206}\)

\(A=\dfrac{6.3}{2.5}+\dfrac{6.3}{5.8}+...+\dfrac{6.3}{203.206}\)

\(A=6\left(\dfrac{3}{2.5}+\dfrac{3}{5.8}+...+\dfrac{3}{203.206}\right)\)

\(A=6\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+...+\dfrac{1}{203}-\dfrac{1}{206}\right)\)

\(A=6\left(\dfrac{1}{2}-\dfrac{1}{206}\right)\)

\(A=6.\dfrac{51}{103}\)

\(A=\dfrac{306}{103}\)

18/(2.5) + 18/(5.8) + .... + 18/(203.206)

= 18.[1/(2.5) + 1/(5.8) + .... + 1/(203.206)]

= 18.(1/2 - 1/5 + 1/5 - 1/8 + .... + 1/203 - 1/206)

=18.(1/2 - 1/206)

=18.(51/103)

=918/103

a) \(\frac{4}{3.5}+\frac{4}{5.7}+...+\frac{4}{97.99}\)

\(=4.\left(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{97.99}\right)\)

\(=4.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}\right)\)

\(=4.\left(\frac{1}{3}-\frac{1}{99}\right)\)

\(=4.\frac{32}{99}\)

\(=\frac{128}{99}\)

\(\frac{4}{3.5}+\frac{4}{5.7}+...+\frac{4}{97.99}\)

\(=2\left(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99}\right)\)

\(=2\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}\right)\)

\(=2\left(\frac{1}{3}-\frac{1}{99}\right)\)

\(=2.\frac{32}{99}\)

\(=\frac{64}{99}\)

\(\frac{18}{2.5}+\frac{18}{5.8}+...+\frac{18}{203.206}\)

\(=6\left(\frac{3}{2.5}+\frac{3}{5.8}+...+\frac{3}{203.206}\right)\)

\(=6\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{203}-\frac{1}{206}\right)\)

\(=6\left(\frac{1}{2}-\frac{1}{206}\right)\)

\(=6.\frac{102}{206}\)

\(=\frac{612}{206}\) ( tự rút gọn

\(\frac{18}{2.5}+\frac{18}{5.8}+....+\frac{18}{103.106}\)

=\(6\left(\frac{3}{2.5}+\frac{3}{5.8}+....+\frac{3}{103.106}\right)\)

=\(6\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+....+\frac{1}{103}-\frac{1}{106}\right)\)

=\(6\left(\frac{1}{2}-\frac{1}{106}\right)\)

=\(6.\frac{26}{53}\)

=\(\frac{156}{53}\)

khó thế ko giải được

609/205

`@` `\text {Ans}`

`\downarrow`

\(\dfrac{7}{5}\cdot\dfrac{8}{19}+\dfrac{7}{5}\cdot\dfrac{12}{19}-\dfrac{7}{5}\cdot\dfrac{1}{18}\)

`=`\(\dfrac{7}{5}\cdot\left(\dfrac{8}{19}+\dfrac{12}{19}-\dfrac{1}{18}\right)\)

`=`\(\dfrac{7}{5}\cdot\left(\dfrac{20}{19}-\dfrac{1}{18}\right)\)
`=`\(\dfrac{7}{5}\cdot\dfrac{341}{342}=\dfrac{2387}{1710}\)

\(\frac{9^{14}.25^5.8^7}{18^{12}.625^3.24^3}\)

\(=\frac{\left(3^2\right)^{14}.\left(5^2\right)^5.\left(2^3\right)^7}{\left(2.3^2\right)^{12}.\left(5^4\right)^3.\left(2^3.3\right)^3}\)

\(=\frac{3^{28}.5^{10}.2^{21}}{2^{12}.3^{24}.5^{12}.2^9.3}\)

\(=\frac{3^{28}.5^{10}.2^{21}}{2^{21}.3^{25}.5^{12}}\)

\(=\frac{3^3.1.1}{1.1.5^2}\)

\(=\frac{27}{25}\)