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a) (x + 73) - 26 = 76
x + 73 = 76 + 26
x + 73 = 102
x = 102-73
x = 29
b) 45-(c + 9) = 6
c + 9 = 6 + 45
c + 9 =51
c =51 - 9
c = 42
c) 89 - (73 - x)= 20
73 - x = 89 - 20
73 - x = 69
x = 73 - 69
x = 4
d) (x + 7) - 25 = 13
x + 7 = 13 + 25
x + 7 = 38
x = 38 - 7
x = 31
e) 198 - (x + 4) = 120
x + 4 = 198 - 120
x + 4 = 68
x = 68 - 4
x = 64
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A = 2 x 53 x 12 + 4 x 6 x 87 - 3 x 8 x 40
= 24 x 53 + 24 x 87 - 24 x 40
= 24 x ( 53 + 87 - 40 )
= 24 x 100
= 2400
B = 5 x 7 x 77 - 7 x 60 + 49 x 25 - 15 x 42
= 5 x 7 x 77 - 7 x 5 x 12 + 49 x 5 x 5 - 5 x 3 x 42
= 5 x 539 - 84 x 5 + 245 x 5 - 5 x 126
= 5 x ( 539 - 84 + 245 - 126 )
= 5 x 574
= 2870
a=2×53×12+4×6×87-3×8×40
a=24×53+24×87-24×40
a=24×(53+87-40)
a=24×100
a=2400
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(1+x)+(2+x)+(4+x)+(7+x)+...+(22+x)=77
=> (1+2+4+7+...+22)+(x+x+x+x+...+x)=77 ( 7 số hạng x)
=> 63 + 7x =77
=> 7x =77-63
=> 7x =14
=> x = 14:7
=> x =2
Vậy x = 2
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( x+1 )+ ( x +2 ) +( x + 3 ) + ( x + 4 ) + ....( + 12 ) = 77
( x + x + x + ... + x ) + ( 1 + 2 + 3 + ... + 12 ) = 77
12x + 78 = 77
12x = -1
x = -1/12
=> (x + x + x + x +...+x) + (1+2+3+4+...+12) = 77
Đặt A = (x+x+x+x+...+x); B = 1+2+3+4+...+12
Số số hạng của B là : (12 - 1) : 1 + 1 = 12 (sh)
Tổng B là : (1 + 12) . 12 : 2 = 78
Vì B có 12 sh nên A có 12x
=> 12x + 78 = 77
=> 12x = 77 - 78
=> 12x = -1
=> x = -1/12
Vậy
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1/2 x 2/8 x 3/28 x 4/77 x 5/176
\(=\frac{1.2.3.4.5}{2.8.28.77.176}=\frac{1.2.3.4.5}{2.2.4.7.4.11.4.4}=\frac{3.5}{2.7.4.4.11.4}=\frac{15}{9856}\)
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\(A=1\frac{4}{5}\times1\frac{4}{21}\times1\frac{4}{45}\times...\)
Ta có: \(1\frac{4}{5}=\frac{5+4}{5}=\frac{9}{5}=\frac{3\times3}{1\times5}\)
\(1\frac{4}{21}=\frac{21+4}{21}=\frac{25}{21}=\frac{5\times5}{3\times7}\)
\(1\frac{4}{45}=\frac{45+4}{45}=\frac{49}{45}=\frac{7\times7}{5\times9}\)
...
Tổng quát thừa số thứ \(n\)là: \(\frac{\left(2\times n+1\right)\times\left(2\times n+1\right)}{\left(2\times n-1\right)\times\left(2\times n+3\right)}\)
Thừa số thứ \(100\)là: \(\frac{201\times201}{199\times203}\).
Tích \(A\)là:
\(A=\frac{3\times3}{1\times5}\times\frac{5\times5}{3\times7}\times\frac{7\times7}{5\times9}\times...\times\frac{201\times201}{199\times203}\)
\(=\frac{\left(3\times5\times7\times...\times201\right)\times\left(3\times5\times7\times...\times201\right)}{\left(1\times3\times5\times...\times199\right)\times\left(5\times7\times9\times...\times203\right)}\)
\(=\frac{201\times3}{1\times203}=\frac{603}{203}\)
\(\frac{4}{6.7}+\frac{4}{7.8}+...+\frac{4}{72.73}=4\left(\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{72.73}\right)\)
\(=4\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{72}-\frac{1}{73}\right)=4\left(\frac{1}{6}-\frac{1}{73}\right)=\frac{268}{438}=\frac{134}{219}\)
\(\frac{4}{6x7}+\frac{4}{7x8}+...+\frac{4}{72x73}\)
\(=4x\left(\frac{1}{6x7}+\frac{1}{7x8}+...+\frac{1}{72x73}\right)\)
\(=4x\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{72}-\frac{1}{73}\right)\)
\(=4x\left(\frac{1}{6}-\frac{1}{73}\right)\)
\(=4x\frac{67}{438}\)
\(=\frac{268}{438}\)
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