$a$) $201,2 + 2 \times 201,2 + 3 \times 201,2 + 4 \times 201,24

$= 201,2 \times (1+2+3+4)$

$= 201,2 \times 10$

$= 2012$

$b$) $\dfrac{3}{1 \times 2} + \dfrac{3}{2 \times 3} + \dfrac{3}{3 \times 4} + ... + \dfrac{3}{99 \times 100}$

$= 3.(\dfrac{1}{1 \times 2} + \dfrac{1}{2 \times 3} + \dfrac{1}{3 \times 4} + ... + \dfrac{1}{99 \times 100})$

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

$= 3(1 - \dfrac{1}{100})$

$= 3 - \dfrac{3}{100}$

$= \dfrac{297}{100}$

$c$) $3,54 \times 73 + 0,46 \times 12,5 + 3,54 \times 26 + 0,17 \times 25 + 3,54$

$= 3,54 \times (73 + 26 + 1) + 25 \times (0,23 + 0,17)$

$= 3,54 \times 100 + 25 \times 0,4$

$= 354 + 10$

$= 364$

$d$) $A = \dfrac{1}{2} + \dfrac{5}{6} + \dfrac{11}{12} + \dfrac{19}{20} + \dfrac{29}{30} + \dfrac{41}{42} + \dfrac{55}{56} + \dfrac{71}{72} + \dfrac{89}{90}$

$A = (1- \dfrac{1}{2}) + (1 - \dfrac{1}{6}) + (1 - \dfrac{1}{12}) + (1 - \dfrac{1}{20}) + (1 - \dfrac{1}{30}) + (1- \dfrac{1}{42}) + (1 - \dfrac{1}{56}) + (1 - \dfrac{1}{72}) + (1 - \dfrac{1}{90})$

$A = (1+1+1+1+1+1+1+1+1) - (\dfrac{1}{2} + \dfrac{1}{6} + \dfrac{1}{12} + \dfrac{1}{20} + \dfrac{1}{30} + \dfrac{42} + \dfrac{56} + \dfrac{72} + \dfrac{1}{90})$

$A = 9 - (\dfrac{1}{1.2} + \dfrac{1}{2.3} + \dfrac{1}{3.4} + ... + \dfrac{1}{8.9} + \dfrac{1}{9.10})$

$A = 9 - (1 - \dfrac{1}{10})$

$A = 8 + \dfrac{1}{10}$

$A = \dfrac{81}{10}$

$e$) $\dfrac{1995 \times 1994 - 1}{1993 \times 1995 + 1994}$

$= \dfrac{1995 \times 1993 + 1995 -1}{1993 \times 1995 + 1994}$

$= \dfrac{1995 \times 1993 + 1994}{1993 \times 1995 + 1994}$

$= 1$

$h$) $\dfrac{373737}{474747} + \dfrac{5757}{4747}$

$= \dfrac{37}{47} + \dfrac{57}{47}$

$= \dfrac{94}{47}$

$=2$

Đáp án:

Giải thích các bước giải:

a) 201,2 + 2 x 201,2 + 3 x 201,2 + 4 x 201,2

= 201,2 x (1 + 2 + 3 + 4)

= 201,2 x 10

= 2012

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

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

= 3 x (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

c) 3,54 x 73 + 0,46 x 12,5 + 3,54 x 26 + 0,17 x 25 + 3,54

= 3,54 x (73 + 26 + 1) + 0,46 x 12,5 + 0,17 x 25

= 3,54 x 100 + 5,75 + 4,25

= 354 + 10

= 364

d)

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

A = (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)

A = 1 x 9 - (1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90)

A = 9 - (1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 + 1/6x7 + 1/7x8 + 1/8x9 + 1/9x10)

A = 9 - (1 - 1/2 + 1/2 - 1/3 +... +1/9 - 1/10)

A = 9 - (1 - 1/10)

A = 9 - 9/10

A = 81/10

e) Chịu... (vì lâu chưa làm lại...TT-TT)

h) 373737/474747 + 5757/4747

= 37x10101/47x10101 + 57x101/47x101

= 37/47 + 57/47

= 94/47