tính nhanh
1000 + 110 + 10 + 90
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1/2 + 5/6 + 11/12 + ... + 89/90 + 109/110 + 10/11
= (1 - 1/2) + (1 - 1/6) + (1 - 1/12) + ... + (1 - 1/90) + (1 - 1/110) + 10/11
= (1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1) - (1/1*2 + 1/2*3 + 1/3*4 + ... + 1/10*11) + 10/11
= 9 - (1 - 1/11) + 10/11
= 9 - 10/11 + 10/11 = 9
\(A=\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{6}\right)+\left(1-\frac{1}{12}\right)+....+\left(1-\frac{1}{90}\right)+\left(1-\frac{1}{110}\right)+\frac{10}{11}\)
\(=10-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{10.11}\right)+\frac{10}{11}=10-\left(1-\frac{1}{11}\right)+\frac{10}{11}=10\)
110 -10 > X5 + 5X > 90
100 > X0 + 5 + 50 + X > 90
100 > XX + 55 > 90
100 - 55 > XX + 55 - 55 > 90 - 55
45 > XX > 35
XX = 44 SUY RA X = 4
\(\frac{1}{10}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{90}+\frac{1}{110}\)
\(=\frac{1}{10}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{9.10}+\frac{1}{10.11}\)
\(=\frac{1}{10}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)
\(=\frac{1}{10}+\frac{1}{4}-\frac{1}{11}\)
\(=\frac{57}{220}\)
\(\frac{1}{10}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{90}+\frac{1}{110}\)
\(=\frac{1}{10}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{9.10}+\frac{1}{10.11}\)
\(=\frac{1}{10}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)
\(=\frac{1}{10}+\frac{1}{4}-\frac{1}{11}\)
\(=\frac{22}{220}+\frac{55}{220}-\frac{20}{220}\)
\(=\frac{22+55-20}{220}\)
\(=\frac{57}{220}\)
t=(1-1/2+1-1/6+1-1/12+..........+1-1/90+1-1/110)-10/11
t=(1+1+1+...........+1+1)-(1/2+1/6+1/12+.......+1/90+1/110)-10/11
có 10 số 1 vì từ 1/2 đến 109/110 có 10 p/số
t=1.10-(1/1.2+1/2.3+1/3.4+.........+1/9.10+1/10.11)-10/11
t=10-(1-1/2+1/2_1/3+1/3_1/4+.............+1/9-1/10+1/10-1/11)-10/11
t=10-(1-1/11)-10/11
t=10-10/11-10/11
t=10-(10/11+10/11)
t=10-10/11.2
t=10-20/11
t=110/11-20/11
t=90/11
Đặt A=90+110+132+...+930
=9.10+10.11+11.12+...+30.31
=>3A=3.9.10+3.10.11+...+3.30.31
=9.10.11-8.9.10+10.11.12-9.10.11+....+30.31.32-29.30.31
=30.31.32-8.9.10
=29040
=>A=29040:3=9680
1000 + 110 + 10 + 90
= ( 90 + 10 ) + ( 1000 + 110 )
= 100 + 1110 = 1210
1000 + 110 + 10 + 90
= 1110 + 10 + 90
= 1120 + 90
= 1210
Ủng hộ nha ~