Tính
A=1/2×9+1/9×7+1/7×19+...+1/252×509
B=1/10×9+1/18×13+1/26×17+...+1/802×405
C=2/4×7-3/5×9+2/7×10-3/9×13+...+2/301×304-3/401×405
Bài 1;tính
A=1/2*9+1/9*7+1/7*19+....+1/252*509
B=1/10*9+1/18*13+/26*17+....+1/802*405
C=2/4*7-3/5*9+2/7*10-3/9*13+...+2/301*304-3/401*405
Bài 2
Cho S=1/5^2+1/9^2+...+1/409^2
Chứng minh S<1/12
4S = 4/(5x5) + 4/(9x9) + … + 1/(409x409)
Ta thấy:
4/(5x5) < 4/(3x7) = 1/3 – 1/7
4/(9x9) < 4/(7x11) = 1/7 – 1/11
…………
4/(409x409) < 4/(407x411) = 1/407 – 1/411
Mà :
4/(3x7) + 4/(7x11) + …. + 4/(407x411) = 1/3 – 1/411 = 136/411
4S < 136/411
S < 34/411 < 34/408 = 1/12
Hay S < 1/12
C=2/4×7-3/5×9+2/7×10-3/9×13+...+2/301×304-3/401×405
R = 1/10*9 + 1/ 18*13 +....+ 1/ 802 * 405
S = 2/4*7 - 3/5*9 + 2/7*10 - 3/9*13
Ráng giúp mk nha mk dg cần gấp !!!
\(S=\dfrac{2}{4\cdot7}+\dfrac{2}{7\cdot10}-\dfrac{3}{5\cdot9}-\dfrac{3}{9\cdot13}\)
\(=\dfrac{2}{3}\left(\dfrac{3}{4\cdot7}+\dfrac{3}{7\cdot10}\right)-\dfrac{3}{4}\left(\dfrac{4}{5\cdot9}+\dfrac{4}{9\cdot13}\right)\)
\(=\dfrac{2}{3}\left(\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}\right)-\dfrac{3}{4}\cdot\left(\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}\right)\)
\(=\dfrac{2}{5}\cdot\dfrac{3}{20}-\dfrac{3}{4}\cdot\dfrac{8}{65}=\dfrac{-21}{650}\)
Bài 1: Tính
a) -3/20 + -7/4
b) 6 2/3 - 4 2/3
c) -3/10 + 7/12
d) 35/-9 . 81/7
e) -2/5 - -3/4
f) 5/23 . 7/26 + 5/23 . 9/26
g) -3/12 : 4/15
h) 1 1/6 - 3 1/3
i) -2/5 . (-3) + 3/8 . 4/-10
j) -13/17 + (13/-21 + -4/17)
a) \(\dfrac{-3}{20}\) + \(\dfrac{-7}{4}\) =\(\dfrac{-3}{20}\) + \(\dfrac{-35}{20}\) = -2
b) 6 và \(\dfrac{2}{3}\) - 4 và \(\dfrac{2}{3}\) = 2
c) \(\dfrac{-3}{10}\) + \(\dfrac{7}{12}\) = \(\dfrac{-18}{60}\) + \(\dfrac{35}{60}\) =\(\dfrac{17}{60}\)
d) \(\dfrac{35}{-9}\) . \(\dfrac{81}{7}\) = \(\dfrac{-35}{9}\) . \(\dfrac{81}{7}\) = 45
e) \(\dfrac{-2}{5}\) - \(\dfrac{-3}{4}\) = \(\dfrac{-8}{20}\) - \(\dfrac{-15}{20}\) = \(\dfrac{-8}{20}\) + \(\dfrac{15}{20}\) =\(\dfrac{7}{20}\)
f) \(\dfrac{5}{23}\) . \(\dfrac{7}{26}\) + \(\dfrac{5}{23}\) .\(\dfrac{9}{26}\) = \(\dfrac{5}{23}\) . ( \(\dfrac{7}{26}\) + \(\dfrac{9}{26}\) )= \(\dfrac{5}{23}\) . \(\dfrac{8}{13}\) = \(\dfrac{40}{299}\)
g) \(\dfrac{-3}{12}\) : \(\dfrac{4}{15}\) =\(\dfrac{-3}{12}\) . \(\dfrac{15}{4}\) =\(\dfrac{-5}{8}\)
h) 1 và \(\dfrac{1}{6}\) - 3 và \(\dfrac{1}{3}\) =\(\dfrac{7}{6}\) -\(\dfrac{10}{3}\) = \(\dfrac{-13}{6}\)
i) \(\dfrac{-2}{5}\) . (-3) + \(\dfrac{3}{8}\) . \(\dfrac{4}{-10}\) =(\(\dfrac{-2}{5}\) .\(\dfrac{-4}{10}\)) + [(-3) . \(\dfrac{3}{8}\)
= \(\dfrac{4}{25}\) + \(\dfrac{-9}{8}\) = \(\dfrac{32}{200}\) + \(\dfrac{-225}{200}\) = \(\dfrac{-193}{200}\)
j) \(\dfrac{-13}{17}\) + (\(\dfrac{13}{-21}\) + \(\dfrac{-4}{17}\) )
= ( \(\dfrac{-13}{17}\) + \(\dfrac{-4}{17}\) )+\(\dfrac{-13}{21}\)
= -1+\(\dfrac{-13}{21}\)
= \(\dfrac{-21}{21}\) + \(\dfrac{-13}{21}\) = \(\dfrac{-34}{21}\)
Khôi nguyễn
4.24.5^2-(3^3.18+3^3.12)
31.15.7^2.4-31.49.40
1+2+3+4+5+6+7+8+9+10
1+3+5+7+9+11+13+15+19
2+6+10+14+22+23+26+34
5+8+11+14+17+20+23+26+29
1+6+11+16+21+26+31+36+41+47+51
10+13+16+19+22+25+28+31+34+37+40
5+7+9+11+13+15+17+3+8+13+18+23+28
4+7+10+13+16+19+5+9+13+17+21+25
4.24.52-(33.18+33.12)
=4.24.25-[27.(18+12)]
=(4.25).24-[27.30]
=100.24-810
=2400-810
=1590
4.24.5^2-(3^3.18+3^3.12)
31.15.7^2.4-31.49.40
1+2+3+4+5+6+7+8+9+10
1+3+5+7+9+11+13+15+19
2+6+10+14+22+23+26+34
5+8+11+14+17+20+23+26+29
1+6+11+16+21+26+31+36+41+47+51
10+13+16+19+22+25+28+31+34+37+40
5+7+9+11+13+15+17+3+8+13+18+23+28
4+7+10+13+16+19+5+9+13+17+21+25 = 1590
#HT#
Tính:
1, 7/36- 8/-9 + -2/3
2, -1/2 + 3/7 - 1/9 + -7/18 + 4/7
3, -10/3 + 13/10 - 1/6 + 1/10
4, 10/17- 5/13 - (-7/17) - 8/13 + 11/25
\(1.\) \(\dfrac{7}{36}-\dfrac{8}{-9}+\dfrac{-2}{3}=\dfrac{7}{36}+\dfrac{8}{9}-\dfrac{2}{3}=\dfrac{7+32-24}{36}=\dfrac{5}{12}.\)
\(2.\) \(\dfrac{-1}{2}+\dfrac{3}{7}-\dfrac{1}{9}+\dfrac{-7}{18}+\dfrac{4}{7}=\dfrac{-9-2-7}{18}+\dfrac{4+3}{7}=\dfrac{-18}{18}+\dfrac{7}{7}=-1+1=0.\)
\(3.\) \(-\dfrac{10}{3}+\dfrac{13}{10}-\dfrac{1}{6}+\dfrac{1}{10}=\dfrac{13+1}{10}+\dfrac{-20-1}{6}=\dfrac{14}{10}+\dfrac{-21}{6}=\dfrac{7}{5}-\dfrac{7}{2}=-\dfrac{21}{10}.\)
\(4.\) \(\dfrac{10}{17}-\dfrac{5}{13}-\left(-\dfrac{7}{17}\right)-\dfrac{8}{13}+\dfrac{11}{25}=\dfrac{10+7}{17}+\dfrac{-5-8}{13}+\dfrac{11}{25}=\dfrac{17}{17}-\dfrac{13}{13}+\dfrac{11}{25}=\dfrac{11}{25}.\)
Tính:
1, 7/36- 8/-9 + -2/3
2, -1/2 + 3/7 - 1/9 + -7/18 + 4/7
3, -10/3 + 13/10 - 1/6 + 1/10
4, 10/17- 5/13 - (-7/17) - 8/13 + 11/25
1: \(=\dfrac{7}{36}+\dfrac{32}{36}+\dfrac{-24}{36}=\dfrac{15}{36}=\dfrac{5}{12}\)
2: \(=\left(-\dfrac{1}{2}-\dfrac{1}{9}-\dfrac{7}{18}\right)+\dfrac{3}{7}+\dfrac{4}{7}\)
\(=\dfrac{-9-2-7}{18}+1=-1+1=0\)
3: \(=\left(-\dfrac{10}{3}-\dfrac{1}{6}\right)+\dfrac{14}{10}\)
\(=-\dfrac{21}{6}+\dfrac{14}{10}=\dfrac{-7}{2}+\dfrac{14}{10}=\dfrac{-35+14}{10}=-\dfrac{21}{10}\)
4: \(=\left(\dfrac{10}{17}+\dfrac{7}{17}\right)-\left(\dfrac{5}{13}+\dfrac{8}{13}\right)+\dfrac{11}{25}=\dfrac{11}{25}\)
Tính:
a) -5/7(14/5 - 7/10) : |-2/3| - 3/4(8/9 + 16/3) + 10/3(1/3 + 1/5)
b) 17/-26(1/6 - 5/3) : 17/13 - 20/3(2/5 - 1/4) + 2/3(6/5 - 9/2)
c) -8/9(9/8 - 3/2) + 5/4 : (5/2 - 15/4) - 3/4(10/9 - 8/3) : (-1/3)
d) 21/10 : (12/5 - 9/10) . (-4/7) - 3/2(1/6 - 7/12) + 1/5(3/2 - 1/4)
a) Ta có: \(\dfrac{-5}{7}\left(\dfrac{14}{5}-\dfrac{7}{10}\right):\left|-\dfrac{2}{3}\right|-\dfrac{3}{4}\left(\dfrac{8}{9}+\dfrac{16}{3}\right)+\dfrac{10}{3}\left(\dfrac{1}{3}+\dfrac{1}{5}\right)\)
\(=\dfrac{-5}{7}\cdot\dfrac{3}{2}\cdot\dfrac{21}{10}-\dfrac{3}{4}\cdot\dfrac{56}{3}+\dfrac{10}{3}\cdot\dfrac{8}{15}\)
\(=\dfrac{-9}{4}-14+\dfrac{16}{9}\)
\(=\dfrac{-1621}{126}\)
b) Ta có: \(\dfrac{17}{-26}\cdot\left(\dfrac{1}{6}-\dfrac{5}{3}\right):\dfrac{17}{13}-\dfrac{20}{3}\left(\dfrac{2}{5}-\dfrac{1}{4}\right)+\dfrac{2}{3}\left(\dfrac{6}{5}-\dfrac{9}{2}\right)\)
\(=\dfrac{-17}{26}\cdot\dfrac{13}{17}\cdot\dfrac{-3}{2}-\dfrac{20}{3}\cdot\dfrac{3}{20}+\dfrac{2}{3}\cdot\dfrac{-33}{10}\)
\(=\dfrac{3}{4}-1-\dfrac{11}{5}\)
\(=-\dfrac{49}{20}\)
1+2-3-4+5+6-7-8+9+10-11-12+13+14-15-16+17+18-19-20...+301+302
1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + 9 + ... + 301 + 302 (có 302 số; 302 chia 4 dư 2)
= 1 + (2 - 3 - 4 + 5) + (6 - 7 - 8 + 9) + ... + (288 - 299 - 300 + 301) + 302
= 1 + 0 + 0 + ... + 0 + 302
= 1 + 302
= 303
1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + 9 + ....... +301 + 302 ( có 302 số : 302 chia 4 dư 2 )
= 1 + ( 2 - 3 - 4 + 5 ) + ( 6 - 7 - 8 + 9 ) + ..... + ( 288 - 299 -300 + 301 ) + 302
= 1 + 0 + 0 + ......... + 0 + 302
= 1 + 302
= 303