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A = (4+\(\frac{1}{5}\)) . \(\frac{18}{19}\)+ (2+\(\frac{8}{5}\)) . \(\frac{21}{5}\)
A= \(\frac{21}{5}\).18/19 + 18/5 . 21/5
A= 21/5 (18/19 + 18/5)
A= 21/5 . 432/95
A= 9288/95
b= 25/2. (3+2/7) - 23/7. (5 + 1/2)
b= 25/2 . 23/7 - 23/7 . 11/2
b= 23/7 (25/2 -11/2)
b=23/7 . 7
b= 23
a,\(\frac{21}{25}.\frac{11}{9}.\frac{5}{7}=\frac{21.11.5}{25.9.7}=\frac{3.7.11.5}{5^2.3^2.7}=\frac{11}{5.3}=\frac{11}{15}\)
b,\(\frac{5}{23}.\frac{17}{26}+\frac{5}{23}.\frac{9}{26}=\frac{5}{23}.\left(\frac{17}{26}+\frac{9}{26}\right)=\frac{5}{23}.1=\frac{5}{23}\)
c, \(\left(\frac{3}{29}-\frac{1}{5}\right).\frac{29}{3}=\frac{3}{29}.\frac{29}{3}-\frac{1}{5}.\frac{29}{3}=1-\frac{29}{15}=-\frac{14}{15}\)
a , \(\frac{21}{25}\times\frac{11}{9}\times\frac{5}{7}\)
\(=\frac{21\times11\times5}{25\times9\times7}\)
\(=\frac{3\times7\times11\times5}{5\times5\times3\times3\times7}\)
\(=\frac{11}{5\times3}\)
\(=\frac{11}{15}\)
b , \(\frac{5}{23}\times\frac{17}{26}+\frac{5}{23}\times\frac{9}{26}\)
\(=\frac{5}{23}\times\left(\frac{17}{26}+\frac{9}{26}\right)\)
\(=\frac{5}{23}\times\frac{26}{26}\)
\(=\frac{5}{23}\times1\)
\(=\frac{5}{23}\)
c , \(\left(\frac{3}{29}-\frac{1}{5}\right)\times\frac{29}{3}\)
\(=\frac{3}{29}\times\frac{29}{3}-\frac{1}{5}\times\frac{29}{3}\)
\(=1-\frac{29}{15}\)
a, \(A=\frac{22}{27}\)
b,\(B=\frac{1}{57}\)
C,\(C=\frac{1}{50}\)
d, \(D=0\)
Câu a:
A = -1/2 - (-3)/5 + (-1/9) + 1/27 + 7/18 + 4/35 - (-2/7)
A = -1/2 + 3/5 - 1/9 + 1/27 + 7/18 + 4/35 + 2/7
A = (-1/2 - 1/9 + 7/18 + 1/27) + (3/5 + 4/35 + 2/7)
A = (-27/54 - 6/54 + 21/54 + 2/54) + (21/35 + 4/35 + 10/35)
A = -10/54 + 1
A = -5/27 + 1
A = 22/27
\(E=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}.\frac{5^2}{4.6}...\frac{9^2}{8.10}=\frac{\left(2.3.4...9\right)^2}{1.2.\left(3.4...8\right)^2.9.10}=\frac{2^2.9^2}{1.2.9.10}=\frac{18}{10}=\frac{9}{5}\)
Câu a:
A = (1\(\frac16\) x \(\frac67\) x 6 : \(\frac35\)) : (4\(\frac15\) x \(\frac{10}{11}\) + 5\(\frac{2}{10}\))
A = (7/6 x 6/7 x 6 x 5/3) :(21/5 x 10/11 + 52/10)
A = (1 x 6 x 5/3) : (210/55 + 26/5)
A = 10 : (210/55 + 286/55)
A = 10 : (496/55)
A = 10 x 55/496
A = 275/248
Câu b:
B = \(1\)\(\frac{13}{15}\) x 25% x 3 + (8/15 - 79/60) : 1\(\frac{23}{4}\)
B = 28/15 x 1/4 x 3 + (32/60 - 79/60) : 27/4
B = 7/15 x 3 - 47/60 x 4/27
B = 7/5 - 47/405
B = 104/81
1, =\(\frac{2\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{9}-\frac{1}{11}\right)}{4\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{9}-\frac{1}{11}\right)}=\frac{1}{2}\)
2, A=\(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{99}{100}\)
= \(\frac{1\cdot2\cdot3\cdot....\cdot99}{2\cdot3\cdot4\cdot...\cdot100}=\frac{1}{100}\)
Vậy ......
hok tốt
Bài 1a:
A = \(\frac{7^2}{7.8}\times\frac{8^2}{8.9}\times\ldots\times\frac{11^2}{11.12}\)
A = \(\frac{7.8.9.\ldots11}{7.8.\ldots11}\) x \(\frac{7.8.9\ldots11}{8.9.12}\)
A = 7/12
Bài 1B
B = (1+ 1/11).(1 + 1/12)...(1+ 1/15)
B = (11/11 + 1/11).(12/12 + 1/12)...(15/15+ 1/15)
B = 12/11.13/12....16/15
B = 16/11
A =(1/2 +1)×(1/3 +1)×(1/4 +1)×....×(1/99 +1)
=3/2x4/3x...............x100/99
=2-1/99
=197/99
A= \(\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdot.....\cdot\frac{100}{99}\)
A=\(\frac{\left(3\cdot4\cdot5\cdot....\cdot99\right)\cdot100}{2\cdot\left(3\cdot4\cdot5\cdot...\cdot99\right)}\)
A=\(\frac{100}{2}=50\)
\(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{97\cdot99}\)
\(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}\)
=> \(\frac{1}{3}-\frac{1}{99}=\frac{32}{99}\)>\(\frac{32}{100}\)=32%
\(B=\frac{12}{11}x\frac{13}{12}x.......x\frac{16}{15}\)
\(=\frac{16}{11}\)
Bài 1a:
A = \(\frac{7^2}{7.8}\times\frac{8^2}{8.9}\times\ldots\times\frac{11^2}{11.12}\)
A = \(\frac{7.8.9.\ldots11}{7.8.\ldots11}\) x \(\frac{7.8.9\ldots11}{8.9.12}\)
A = 7/12
Ai xong trước thì mình tick nhé
S = 2/(1×3) + 2/(3×5) + 2/(5×7) + ... + 2/(2023×2025)
= (1 - 1/3) + (1/3 - 1/5) + (1/5 - 1/7) + ... + (1/2023 - 1/2025)
= 1 - 1/2025
= 2024/2025
Vậy S = 2024/2025
Để tính giá trị biểu thức \(S\) , ta sử dụng công thức tách phân số tổng quát:
\(\frac{2}{n \times (n + 2)} = \frac{1}{n} - \frac{1}{n + 2}\)
Tách từng phân số trong tổng \(S\) :
\(\frac{2}{1 \times 3} = \frac{1}{1} - \frac{1}{3}\)
\(\frac{2}{3 \times 5} = \frac{1}{3} - \frac{1}{5}\)
\(\frac{2}{5 \times 7} = \frac{1}{5} - \frac{1}{7}\)
...
\(\frac{2}{2023 \times 2025} = \frac{1}{2023} - \frac{1}{2025}\)
Thay các phân số đã tách vào \(S\) :
\(S=\left(1-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{5}\right)+\left(\frac{1}{5}-\frac{1}{7}\right)+\ldots+\left(\frac{1}{2023}-\frac{1}{2025}\right)\)
Triệt tiêu các số hạng đối nhau ở giữa:
\(S = 1 - \frac{1}{2025}\)
\(\Leftrightarrow S=\frac{2024}{2025}\)