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\(B=\frac{1}{1.2.3.4}+\frac{1}{2.3.4.5}+\frac{1}{3.4.5.6}+...+\frac{1}{8.9.10.11}+\frac{1}{9.10.11.12}\)
\(B=\frac{1}{3}\left(\frac{3}{1.2.3.4}+\frac{3}{2.3.4.5}+\frac{3}{3.4.5.6}+...+\frac{3}{8.9.10.11}+\frac{3}{9.10.11.12}\right)\)
\(B=\frac{1}{3}\left(\frac{1}{1.2.3}-\frac{1}{2.3.4}+\frac{1}{2.3.4}-\frac{1}{3.4.5}+...+\frac{1}{9.10.11}-\frac{1}{10.11.12}\right)\)
\(B=\frac{1}{3}\left(\frac{1}{1.2.3}-\frac{1}{10.11.12}\right)\)
\(B=\frac{1}{3}.\frac{73}{440}=\frac{43}{1320}\)
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a) 1/11 + 2/11 + 3/11 + ... + 10/11
= 1 + 2 + 3 + ... + 10 / 11
= (1 + 10).10:2 / 11
= 11.5/11
= 5
b) 1/10×20 + 1/20×30 + 1/30×40 + ... + 1/90×100
= 1/10×10 × (1/1×2 + 1/2×3 + 1/3×4 + ... + 1/9×10)
= 1/100 × (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/9 - 1/10)
= 1/100 × (1 - 1/10)
= 1/100 × 9/10
= 9/1000
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\(3\dfrac{1}{5}\times\dfrac{10}{11}+1\dfrac{2}{11}\\ =\dfrac{16}{5}\times\dfrac{10}{11}+\dfrac{13}{11}\\ =\dfrac{16\times10}{5\times11}+\dfrac{13}{11}\\ =\dfrac{160}{55}+\dfrac{13}{11}\\ =\dfrac{32}{11}+\dfrac{13}{11}\\ =\dfrac{32+13}{11}\\ =\dfrac{45}{11}\)
\(5\dfrac{1}{3}:1\dfrac{2}{3}-1\dfrac{1}{5}\\ =\dfrac{16}{3}:\dfrac{5}{3}-\dfrac{6}{5}\\ =\dfrac{16}{3}\times\dfrac{3}{5}-\dfrac{6}{5}\\ =\dfrac{16\times3}{3\times5}-\dfrac{6}{5}\\ =\dfrac{48}{15}-\dfrac{6}{5}\\ =\dfrac{16}{5}-\dfrac{6}{5}\\ =\dfrac{16-6}{5}\\ =\dfrac{10}{5}\\ =2\)
\(3\dfrac{1}{5}\times\dfrac{10}{11}+1\dfrac{2}{11}\\ =\dfrac{3\times5+1}{5}\times\dfrac{10}{11}+\dfrac{1\times11+2}{11}\\ =\dfrac{16}{5}\times\dfrac{10}{11}+\dfrac{13}{11}\\ =\dfrac{160}{55}+\dfrac{13}{11}\\ =\dfrac{32}{11}+\dfrac{13}{11}\\ =\dfrac{45}{11}\)
\(5\dfrac{1}{3}:1\dfrac{2}{3}-1\dfrac{1}{5}\\ =\dfrac{5\times3+1}{3}:\dfrac{1\times3+2}{3}-\dfrac{1\times5+1}{5}\\ =\dfrac{16}{3}:\dfrac{5}{3}-\dfrac{6}{5}\\ =\dfrac{16}{3}\times\dfrac{3}{5}-\dfrac{6}{5}\\ =\dfrac{16}{5}-\dfrac{6}{5}\\ =\dfrac{10}{5}=2\)
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1, A = 1 + 4 + 7 + . . . + 298
=> phần này dễ tự làm
2, b = 1 . 2 + 2 . 3 + 3 . 4 + . . . + 20 . 21
=> 3b = 1.2.3 + 2.3.3 + 3.4.3 + . . . + 20.21.3
=> 3b = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + . . . + 20.21.(22 - 19)
=> 3b = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 + 2.3.4 + ... + 20.21.22 - 19.20.21
=> 3b = 20.21.22
=> b = 20.21.22/3 = 3080
3, C = 9 . 10 + 10 . 11 + 11 . 12 + . . . + 50 . 51
=> làm như phần b
1 .A = 1 + 4 + 7 + . . . + 298
số số hạng của tổng trên là
(298-1):3+1=100(số hạng)
tổng của của tổng trên là:
\(\frac{\left(298+1\right).100}{2}\)\(=14950\)
mình chỉ làm được câu A hoi
hok tốt
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A = ( 6 : 3/5 - 7/6 * 6/7 ) : ( 21/5 * 10/11 + 57/11 )
A = ( 10 - 1 ) : ( 42/11 + 57/11)
A = 9 : 9
A = 1
B = 59 /10 : 3/2 - ( 7/3 * 9/2 - 2 * 7/3 ) : 7/4
B = 59/15 - ( 21/2 - 14/3 ) : 7/4
B = 59/15 - 35/6 : 7/4
B = 59/15 - 10/3
B = 3/5
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\(\frac{1}{11}+\frac{2}{11}+\frac{3}{11}+\frac{4}{11}+...+\frac{10}{11}\)
\(=\frac{1+2+3+4+...+10}{11}\)
\(=\frac{\frac{10\times\left(10+1\right)}{2}}{11}\)
\(=\frac{55}{11}=5\)
\(\frac{1}{11}+\frac{2}{11}+\frac{3}{11}+\frac{4}{11}+...+\frac{10}{11}=\frac{1+2+3+4+...+10}{11}=\frac{55}{11}=5\)
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(10 - 1 \(\dfrac{1}{6}\) x \(\dfrac{6}{7}\)) : ( 21: \(\dfrac{11}{2}\) + 5\(\dfrac{2}{11}\) )
( 10 \(\dfrac{7}{6}\) x \(\dfrac{6}{7}\) ) : ( 21 : \(\dfrac{11}{2}\) + \(\dfrac{57}{11}\) )
(10 - 1) : ( \(\dfrac{42}{11}\) + \(\dfrac{57}{11}\) )
= 9 : 9
= 1
=> đáp án : 1
=(10 - 1 1/6 x 6/7) : ( 21: 11/2 + 5 2/11)
=( 10 7/6 x 6/7 ) : ( 21 : 11/2 + 57/11)
=(10 - 1) : ( 42/11 + 57/11 )
= 9 : 9
=1
3
3,5