A = 8 - 8² + 8 + 8³ + 8⁴+ ......+ 8⁹⁹

        A = ( 8 - 8 ) + ( 8² + 8³ + 8⁴ +......+ 8⁹⁹ )

        A = 8² + 8³ + 8⁴ +......+ 8⁹⁹

       8A = 8³ + 8⁴ + 8⁵ +.......+ 8¹⁰⁰ 

  8A - A = ( 8³ + 8⁴ +...+ 8¹⁰⁰ ) - ( 8² + 8³ + ...+ 8⁹⁹ )

       7A = 8¹⁰⁰ - 8²

    => A = \(\frac{8^{100}-8^2}{7}\)

VẬY, \(A=\frac{8^{100}-8^2}{7}\)

15/30 x 21/12=450/360=45/36

\(=\dfrac{1}{2}\times\dfrac{7}{4}=\dfrac{1\times7}{2\times4}=\dfrac{7}{8}\)

\(10:0,5+4:0,25+8:0,125\)
\(=10\times2+4\times4+8\times8=20+16+64=100\)

=20+16+64

=100

\(9x-6^{17}:6^{15}=4x+48:12\\ 9x-6^2=4x+4\\ 9x-36=4x+4\\ 9x-4x=36+4\\ 5x=40\\ x=40:5\\ x=8\)

Bài 1 :

Vì ƯCLN ( a , b ) = 14 => a = 14x ; b = 14y

Mà a + b = 42

Thay a = 14x ; b = 14y vào a + b = 42 được

14x + 14y = 42

14 . ( x + y ) = 42

=> x + y = 3

=> ( x , y ) = ( 0 ; 3 ) ; ( 3 ; 0 ) ; ( 1 ; 2 ) ; ( 2 ; 1 )

=> ( a ; b ) = ( 0 ; 42 ) ; ( 42 ; 0 ) ; ( 14 ; 28 ) ; ( 28 ; 14 )

Vậy ( a ; b ) = ( 0 ; 42 ) ; ( 42 ; 0 ) ; ( 14 ; 28 ) ; ( 28 ; 14 )

Link đây nha bạn tham khảo thử

https://sachgiaibaitap.com/sach_giai/giai-sach-bai-tap-toan-lop-6-bai-17-uoc-chung-lon-nhat/

Học tốt nhé 

a) \(\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{99\times100}\)

    \(=\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

      \(=1-\frac{1}{100}\)

          \(=\frac{99}{100}\)

b) \(\frac{3}{1\times4}+\frac{3}{4\times7}+...+\frac{3}{91\times94}\)

 \(=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-...+\frac{1}{91}-\frac{1}{94}\)

   \(=\frac{1}{1}-\frac{1}{94}\)

    \(=\frac{93}{94}\)

1/2x3 + 1/3x4 + ..... + 1/99x100

= 1/2 - 1/3 + 1/3 - 1/4 + ..... + 1/99 - 1/100

= 1/2 - 1/100

= 49/100

3/1x4 + 3/4x7 + .... + 3/91x94

= 3 - 3/4 + 3/4 - 3/7 + .....+ 3/91 - 3/94

= 3 - 3/94

= 279/94

-50

Đặt A = 1 - 2 + 3 - 4 + 5 - 6 + ......+ 97 - 98 + 99 - 100

<=> A = ( 1 - 2 ) + ( 3 - 4 ) + ( 5 - 6 ) + ...... + ( 97 - 98 ) + ( 99 - 100 )

<=> A = ( - 1 ) + ( - 1 ) + ( - 1 ) + ...... + ( - 1 ) + ( - 1 ) ( Có 50 số )

 => A = ( - 1 ) . 50 = - 50

Vậy A = - 50