\(5^{100}-5^{99}-5^{98}=5^{98}\left(5^2-5-1\right)=5^{98}\cdot19=5^{97}\cdot5\cdot19=5^{97}\cdot95⋮95\left(đpcm\right)\)

5¹⁰⁰ - 5⁹⁹ - 5⁹⁸

= 5⁹⁸ (5²-5-1)

=5⁹⁸ . 19

=5⁹⁷ .5 . 19

=5⁹⁷ .95

vì 95 chia hết cho 95

=> 5¹⁰⁰ - 5⁹⁹ - 5⁹⁸  chia hết cho 95

\(P=1+5+5^2+..........+5^{2016}\)

\(\Leftrightarrow5P=5+5^2+5^3+............+5^{2017}\)

\(\Leftrightarrow5P-P=\left(5+5^2+..........+5^{2017}\right)-\left(1+5+..........+5^{2016}\right)\)

\(\Leftrightarrow4P=5^{2017}-1\)

\(\Leftrightarrow P=\dfrac{5^{2017}-1}{4}\)

Mà \(Q=\dfrac{5^{2017}}{4}\)

\(\Leftrightarrow Q-P=\dfrac{5^{2017}}{4}-\dfrac{5^{2017}-1}{4}=\dfrac{5^{2017}-5^{2017}-1}{4}=-\dfrac{1}{4}\)

\(=\dfrac{1}{3}\left(\dfrac{1}{3}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{9}+...+\dfrac{1}{15}-\dfrac{1}{18}\right)\)

\(=\dfrac{1}{3}\left(\dfrac{1}{3}-\dfrac{1}{18}\right)=\dfrac{1}{3}\cdot\dfrac{5}{18}=\dfrac{5}{54}\)

\(\dfrac{5}{54}\)

\(\frac{6}{15.18}+\frac{6}{18.21}+\frac{6}{21.24}+...+\frac{6}{87.90}\)

\(\rightarrow\frac{6}{3}.\left(\frac{3}{15.18}+\frac{3}{18.21}+...+\frac{3}{87.90}\right)\)

\(\rightarrow2.\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{87}-\frac{1}{90}\right)\)

\(\rightarrow2.\left(\frac{1}{15}-\frac{1}{90}\right)\)

\(\rightarrow\frac{1}{9}\)

90.2+45.6+15.18=a

180 + 270 + 270 = a

720 = a

=> a = 720

A = 6/3 . ( 1/15.18 + 1/18.21 + 1/21/24 + . . . + 1/87.90 )

A = 6/3 . ( 1/15 - 1/18 + 1/18 - 1/21 + 1/21 - 1/24 + . . . + 1/87 - 1/90 )

A = 2 . ( 1/15 - 1/90 ) 

A = 2. 5/90

A = 10/90 = 1/9

\(\frac{6}{15.18}+\frac{6}{18.21}+\frac{6}{21.24}+...+\frac{6}{84.87}+\frac{6}{87.90}\)

\(=\frac{6}{3}\left(\frac{3}{15.18}+\frac{3}{18.21}+\frac{3}{21.24}+...+\frac{3}{84.87}+\frac{3}{87.90}\right)\)

\(=2\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{84}-\frac{1}{87}+\frac{1}{87}-\frac{1}{90}\right)\)

\(=2\left(\frac{1}{15}-\frac{1}{90}\right)=2\left(\frac{6-1}{90}\right)=2\times\frac{1}{18}=\frac{1}{9}\)

thầy thiện ơi em ty nè thầy còn nhớ em chăng

( 5¹⁵ . 18 + 5¹⁵ . 7 ) : 5¹⁷

= [5¹⁵ . ( 18 + 15 ) ] : 5¹⁷

= ( 5 ¹⁵ . 33 ) : 5¹⁷

= ( 5¹⁷ : 5¹⁵ ) . 33

= 5² .33

= 25 . 33

= 825

Nhầm sorry : 

( 5¹⁵ . 18 + 5¹⁵ . 7 ) : 5¹⁷

= [ 5¹⁵ . ( 18 + 7 ) ] : 5¹⁷

= ( 5¹⁵ . 25 ) : 5¹⁷

= ( 5¹⁷ : 5¹⁵ ) : 25

= 5² : 25

= 25 : 25

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