Tính tổng :
A=12 +56 +1112 +1920 +2930 +4142 +5556 +7172 +8990
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Sửa đề: \(A=\frac12+\frac56+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}+\frac{55}{56}+\frac{71}{72}+\frac{89}{90}+\frac{109}{110}\)
\(=1-\frac12+1-\frac16+1-\frac{1}{12}+1-\frac{1}{20}+\cdots+1-\frac{1}{110}\)
\(=10-\left(\frac12+\frac16+\frac{1}{12}+\cdots+\frac{1}{110}\right)\)
\(=10-\left(1-\frac12+\frac12-\frac13+\frac13-\frac14+\cdots+\frac{1}{10}-\frac{1}{11}\right)\)
\(=10-\left(1-\frac{1}{11}\right)=10-\frac{10}{11}=\frac{110}{11}-\frac{10}{11}=\frac{100}{11}\)
a: n(omega)=100
n(A)=12
=>P=12/100=3/25
b: n(B)=25+17+13+7=62
=>P(B)=62/100=31/50
c: n(C)=12+6+20+25=63
=>P(C)=63/100
a ) 17 6 b ) − 43 30 c ) − 5 36
d ) 9 20 . e ) 11 3 . f ) 1 12
a) 1 2 + − 2 3 + 1 6 + 3 7 = 3 6 + − 4 6 + 1 6 + 3 7 = 3 7
b) 1 2 + 2 8 + 3 4 + 4 5 + 5 6 = 30 60 + 40 60 + 45 60 + 48 60 + 50 60 = 71 5
a) 1 2 + 2 3 + 3 4 + 4 5 + 5 6 = 30 60 + 40 60 + 45 60 + 48 60 + 50 60 = 71 20
b) 4 6 + 27 81 = 4 6 + 2 6 = 1
a) 3.
b) 1.
c ) 1 2 + − 2 3 + 1 6 + 3 7 = 3 6 + − 4 6 + 1 6 + 3 7 = 3 7 ; d ) 1 2 + 2 8 + 3 4 + 4 5 + 5 6 = 30 60 + 40 60 + 45 60 + 48 60 + 50 60 = 71 5
`= 1 - 1/2 + 1 - 1/6 + ... + 1 - 1/56`
`= 1 - 1/(1.2) + 1 - 1/(2.3) + ... + 1 - 1/(7.8)`
`= 7 - (1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4+ 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8`.
`= 8 - 1/8`
`= 63/64`.
`A=1/2+5/6+11/12+19/20+29/30+41/42+55/56`
`A=1-1/2+1-1/6+1-1/12+1-1/20+1-1/30+1-1/42+1-1/56`
`A=(1+1+1+1+1+1+1)-(1/2+1/6+1/12+....+1/56)`
`A=7-(1/[1xx2]+1/[2xx3]+1/[3xx4]+....+1/[7xx8])`
`A=7-(1-1/2+1/2-1/3+1/3-1/4+....+1/7-1/8)`
`A=7-(1-1/8)`
`A=7-(8/8-1/8)`
`A=7-7/8`
`A=56/8-7/8=49/8`
A = 1/2+5/6+11/12+19/20+29/30+41/42+55/56+71/72+89/90 =
1-1/2+1-1/6+1-1/12+1-1/20+1-1/30+1-1/42+1-1/56+1-1/72+1-1/90 =
9 – (1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90) =
9 – [1/(1x2)+1/(2x3)+1/(3x4)+1/(4x5)+1/(5x6)+1/(6x7)+1/(7x8)+1/(8x9)+1/(9x10)] =
9 – ( 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10) =
9 – (1 – 1/10) = 9 – 9/10 = 81/10