a) 1 + 2 + 3 + ... + 9999 = (9999 + 1) . 9999 : 2 = 49995000
b) 1 + 5 + 9 + ... + 1001 = (1001 + 1) . 501 : 2 = 251001
c) 1/2 . 2/3 . 3/4 . ... . 99/100
= 1.2.3.4.....99/2.3.4.5.6.....100
= 1/100
chứng minh : 100 - ( 1+1/2+1/3+...+1/100) = 1/2+2/3+3/4+..+99/100
Bài 6 : Tính giá trị các biểu thức .
a. A = -5/7 + 7/-5 + 4/7 + 7/4 .
b. B = 2/-5 + -3/7 + -7/10 + 3/-8 .
c. C = -5/7 + 2/-7 + 4/-9 + 4/9 .
d. D = ( 3 - 3/4 + 2/3 ) - ( 2 + 4/3 - 3/2 ) - ( 1 - 7/3 - 9/2 ) .
Tính bằng cách hợp lý nhất : a) -2/3+(-1)/5+3/4-5/6-7/10 b) 0,5+1/3+0,4+5/7+1/6-4/35 c) 1/3+(-1)/5-(-1)/4-7/9-(-5)/12+(-1)/45+1/41
Tính hợp lí nếu có thể:
a)A=10/1/2.(26/1/3-176-7)-12/11.(10/3-1,75)
b)B=(13/84.1,4-2,5.7/180):2/4/9+4/1/2.0,1
c)C=(1-1/4)(1-1/9)(1/16)(1-1/25)...(1-1/10000)
d)D=0,375-0,3+3/11+3/12//-0,625+0,5-5/11-5/12+1,5+1-0,75//2,5+5/3-1,25
1.Tìm x, biết:
a) 7/8 + x = 4/7 b) 6 – x = (-3)/4 c) 1/(-5) + x = 3/4 d) –6 – x = (-3)/5
e) - 2/6 + x = 5/7 f) -8 – x = (-5)/3 g) - 2/10 – x = - 9/8 h) 8 – x = (-1)/6
i) - 2/5 + x = 5/7 j) -2 – x = (-5)/3 k) - 1/6 – x = - 9/8 l) 8 – x = (-1)/5
2. Tính:
a) -7/3 + 4/9 b) -8/18 - 15/56 c) (-7) - (-3/4) d) 0,15 + (-5/12)
e) -1/42 + -1/28 f) -1/21 + -1/36 g) 5,5 - (-2/7) h) 0,9 - (-4/7)
1.Tính :
A = 22 + 42 + 62 + ... + 1002
A = 12 + 32 + 52 + ... + 992
Câu 15 A= 1/3-3/4+3/5+1/2007-1/36+1/25-2/9
Câu 16 A=1/3- 3/4- (-3/5)+ 1/64- 2/9- 1/36+ 1/15
Câu 17 A=1/2- 2/3+ 3/4- 4/5+ 5/6- 6/7- 5/6+ 4/5- 3/4+ 2/3- 1/2
B=\(\frac{1}{3}-\frac{3}{4}-\left(-0,6\right)+\frac{1}{64}-\frac{2}{9}-\frac{1}{36}+\frac{1}{15}\)
C=\(\frac{1}{3}-\frac{3}{5}+\frac{5}{7}-\frac{7}{9}+\frac{9}{11}-\frac{11}{13}+\frac{13}{15}+\frac{11}{15}+\frac{11}{13}-\frac{9}{11}+\frac{7}{9}-\frac{5}{7}+0,6-\frac{1}{3}\)
D=\(\frac{1}{99}-\frac{1}{99.98}-\frac{1}{98.97}.....-\frac{1}{3.2}-\frac{1}{2.1}\)
Tính giá trị biểu thức:
a. \(\dfrac{20^5\times5^{10}}{100^5}\)
b. \(\dfrac{\left(0,9\right)^5}{\left(0,3\right)^6}\)
c. \(\dfrac{6^3+3\times6^2+3^3}{-13}\)
d. \(\dfrac{4^6\times9^5+6^9\times120}{8^4\times3^{12}-6^{11}}\)
e. \(\left(2^{-1}+3^{-1}\right):\left(2^{-1}-3^{-1}\right)+\left(2^{-1}\times2^0\right)\times2^3\)
f. \(\left(\dfrac{-1}{3}\right)^{-1}-\left(\dfrac{-3}{5}\right)^6+\left(\dfrac{1}{2}\right)^2:2\)
