a, = 1

b = 99/100

c = -17/99999995

b) \(\frac{1}{2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)

\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)

\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)

\(1-\frac{1}{100}=\frac{99}{100}\)

a)= 2021.2021-2020.(2021+1)
  = 2021.(2020+1)-2020.(2021+1)
  = (2021.2020)+2021-(2020.2021)-2020
  = 1

b) B= (1+2-3-4)+(5+6-7-8)+(9+10-11-12)...........+(2017+2018-2019-2020)+2021
    B= -4+(-4)+....................(-4)+2021
    B= -4x505+2021
    B= -2020 + 2021
    B = 1

\(B=\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)

   \(=\frac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}}\)

   \(=\frac{2^{29}.3^{18}\left(5.2-3^2\right)}{2^{28}.3^{18}\left(5.3-7.2\right)}\)

   \(=\frac{2^{29}.3^{18}.1}{2^{28}.3^{18}.1}\)

   \(=2\)

Xét tử :

5.4¹⁵.9⁹ - 4.3²⁰.8⁹

= 5.2³⁰.3¹⁸ - 2² . 3²⁰ . 2²⁷

= 5 . 2³⁰ . 3¹⁸ - 2²⁹ . 3²⁰

= 3¹⁸ . 2²⁰ . ( 5 . 2¹⁰ - 2⁹ . 3² )

= 3¹⁸ . 2²⁰ . [ 2⁹ . ( 5 . 2 - 3² ) ]

= 3¹⁸ . 2²⁰ . 2⁹

= 3¹⁸ . 2²⁹

Xét mẫu :

5.2⁹.6¹⁹ - 7.2²⁹.27⁶

= 5 . 2⁹ . 2¹⁹ . 3¹⁹ - 7 . 2²⁹ . 3¹⁸

= 5 . 2²⁸ . 3¹⁹ - 7 . 2²⁹ . 3¹⁸

= 3¹⁸ . 2²⁸ . ( 5 . 3 - 7 . 2 )

= 3¹⁸ . 2²⁸

B = \(\frac{3^{18}.2^{29}}{3^{18}.2^{28}}=2\)

\(\frac{5.4^{15}.9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)

= 1

đúng không ?

\(\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)\(=\frac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}}\)\(=\frac{5.2^{30}.3^{18}-2^{29}.3^{20}}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}\)\(=\frac{2^{29}.3^{18}\left(5.2-3^2\right)}{2^{28}.3^{18}\left(5.3-7.2\right)}=\frac{2.1}{1}=2\)

học tốt ~~~

\(\frac{5\cdot4^{15}\cdot9^9-4\cdot3^{20}\cdot8^9}{5\cdot2^9\cdot6^{19}-7\cdot2^{29}\cdot27^6}\\ =2\)