Đáp án:

Giải thích các bước giải:

a) 3/1 x 2 + 3/2 x 3 + 3/3 x 4 +....+ 3/99x100

=3 x ( 1/1x2 + 1/2x3 + 1/3x4 + ...+ 1/99x100)

=3 x (1/1-1/2+1/2-1/3+1/3-1/4+....+1/99-1/100)

= 3 x ( 1- 1/100) 

= 3 x 99/100

= 297 / 100

b) A = 1/2 + 5/6 + 11/12 + 19/20 + 29/30 + 41/42 + 55/56 + 71/72 + 89/90

= 1 - 1/2 + 1- 1/6 + 1 - 1/ 12 + 1- 1/20 + 1 - 1/ 30 + 1 - 1/42 + 1- 1/56 + 1- 1/72 + 1-1/90

= ( 1 +1+1+1+1+1+1+1+1 ) - ( 1/1 - 1/ 2 + 1/3 - 1/2 +1/3 - 1/4 + 1/5 - 1/4 + 1/5 - 1/6 + 1/7 - 1/6 + 1/7 - 1/8 + 1/9 - 1/8 + 1/9 - 1/10) 

= 9 - ( 1/1 - 1/10 ) 

= 9 - 9 /10

= 81 /10 

c)1995 x 1994 - 1/ 1993 x 1995 + 1994

= 1995 x 1994 - 1/ ( 1994 -1 ) x 1995 + 1994 

= 1995 x 1994 - 1/ 1994 x 1995 - 1995 + 1994 

= 1995 x 1994 - 1/ 1994 x 1995 - 1

= 1

#Nhớ vote sao nhé

#Chúc em học tốt!

Bài 1:

a) 3/1x2 + 3/2x3 + 3/3x4 +...+ 3/99x100

= 3x(1/1x2+1/2x3+1/3x4+1/4x5+...+1/99x100)

= 3x(1/1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100)

= 3x(1-1/100)

= 3x99/100

= 297/100

b) A = 1/2 + 5/6 + 11/12 + 19/20 + 29/30 + 41/42 + 55/56 + 71/72 + 89/90

= 1-1/2+1-1/6+1-1/12+1-1/20+1-1/30+1-1/42+1-1/56+1-1/72+1-1/90

= 9-(1/2+1/6+1/12+1/20+1/30+1/42+1/46+1/72+1/90)

= 9-[1/(1x2)+1/(2x3)+1/(3x4)+1/(4x5)+1/(5x6)+1/(6x7)+1/(7x8)+1/(8x9)+

     1/(9x10)]

= 9-(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-                      1/9+1/9-1/10)

= 9-(1-1/10)

= 9-9/10

= 81/10

c) 1995 x 1994 - 1/ 1993 x 1995 + 1994

= 1995 x 1994 - 1/(1994 - 1) x 1995 + 1994

= 1995 x 1994 - 1/1994 x 1995 - 1995 + 1994

= 995 x 1994 - 1/1994 x 1995 - 1

= 1

( Cho mik câu tlhn nha )