Bài 3: Tính nhanh
a) 01,2 + 2 x 201,2 + 3 x 201,2 + 4 x 201,2
b) 3/1×2 + 3/2×3 + 3/3×4 +…+ 3/99×100
c) 3,54 x 73 + 0,46 x 12,5 + 3,54 x 26 + 0,17 x 25 + 3,54
d) A= 1/2 + 5/6 + 11/12 + 19/20 + 29/30 +41/42 + 55/56 + 71/72 + 89/90
e) 1995 x 1994 – 1/ 1993 x 1995 + 1994
h) 373737/474747 + 5757/4747
$a$) $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) 3/1×2 + 3/2×3 + 3/3×4 +…+ 3/99×100
= 3 x (1/1×2 + 1/2×3 + 1/3×4 +…+ 1/99×100)
= 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 – (1/1×2 + 1/2×3 + 1/3×4 + 1/4×5 + 1/5×6 + 1/6×7 + 1/7×8 + 1/8×9 + 1/9×10)
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
= 37×10101/47×10101 + 57×101/47×101
= 37/47 + 57/47
= 94/47