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Đầu tiên: Rút gọn từng số hạng của A
Tiếp theo: Nhóm lại
Cuối cùng: Ra đáp án
A = 16/9 + 11/9 +9/11 +17/33 +11/39 + 2/13
A= (16/9+11/9) + (9/11+17/33) + (11/39+2/13)
A=3+4/3+17/39=62/13
ta có: 1/2=1/1x2
1/6=1/2x3
1/12=1/3x4
1/20=1/4x5
1/30=1/5x6
1/42=1/6x7
1/56=1/7x8
1/72=1/8x9
1/90=1/9x10
1/110=1/10x11
tiếp theo bn tiếp tục nhé
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110
=1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8+1/8x9+1/9x10+1/10x1
=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+1/10-1/11
=1-1/11
=10/11
a) 52x-3 -2.52 = 52.3
52x.125 = 52.3 + 2.52
52x.125 = 125
52x = 1 = 50
=> 2x = 0 => x =0
b) \(A=\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}+\frac{1}{132}\)
\(A=\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}+\frac{1}{10.11}+\frac{1}{11.12}\)
\(A=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}\)
A = 1/5 - 1/12
A = 7/60
- dễ mà VD : tách 1/30 thành 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9 + 1/9.10 + 1/10.11 +1/11.12 - x =2/3
Ta có:
1/30+1/42+1/56+1/72+1/90+1/110+1/132 -x = 2/3
=>1/(5.6) + 1/(6.7) + 1/(7.8) + (1/8.9) + 1/(9.10) + 1/(10.11) + 1/(11.12) - x = 2/3
=>1/5-1/6+1/6-1/7+...+1/11-1/12 - x = 2/3
=>1/5-1/12 - x = 2/3
=>7/60 - x = 2/3
=> x = 7/60 - 2/3
=> x = -11/20
Ta có:
1/30+1/42+1/56+1/72+1/90+1/110+1/132 -x = 2/3
=>1/(5.6) + 1/(6.7) + 1/(7.8) + (1/8.9) + 1/(9.10) + 1/(10.11) + 1/(11.12) - x = 2/3
=>1/5-1/6+1/6-1/7+...+1/11-1/12 - x = 2/3
=>1/5-1/12 - x = 2/3
=>7/60 - x = 2/3
=> x = 7/60 - 2/3
=> x = -11/20
Ta có A = \(\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}+\dfrac{1}{110}+\dfrac{1}{132}\)
= \(\dfrac{1}{6\cdot7}+\dfrac{1}{7\cdot8}+\dfrac{1}{8\cdot9}+\dfrac{1}{9\cdot10}+\dfrac{1}{10\cdot11}+\dfrac{1}{11\cdot12}\)
= \(\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}\)
= \(\dfrac{1}{6}-\dfrac{1}{12}=\dfrac{1}{12}\)
B = \(\dfrac{\dfrac{2}{29}-\dfrac{2}{39}+\dfrac{2}{49}}{\dfrac{23}{29}-\dfrac{23}{39}+\dfrac{23}{49}}=\dfrac{2\left(\dfrac{1}{29}-\dfrac{1}{39}+\dfrac{1}{49}\right)}{23\left(\dfrac{1}{29}-\dfrac{1}{39}+\dfrac{1}{49}\right)}=\dfrac{2}{23}\)
Lại có \(\dfrac{2}{23}>\dfrac{2}{24}=\dfrac{1}{12}\) hay A < B
Vậy A < B
mình biến đởi phần trong |......| rồi bạn thay vào nha
1/30 + 1/42 + 1/56 + 1/72 +1/ 90 + 1/110 + 1/132
=1/5.6 + 1/6.7 + 1/7.8 + 1/8.9 + 1/9.10 +1/ 10.11
=1/5 -1/6 +1/6 - 1/7 +......+1/10 - 1/11
=1/5 - 1/11=11/55 - 5/55 =6/ 55
thay vào |....|=> |6/55 - x | = 2/3 => mở ra 2 trường hợp mà tính nha
chúc hok tốt
=>(1/5.6+1/6.7+1/7.8+1/9.10+1/10.11+1/11.12)-x=2/3
=>(1/5-1/+1/6-1/7+...+1/11-1/12)-x=2/3
=>(1/5-1/12)-x=2/3
=>7/60-x=2/3
=>x=7/60-2/3
=>x=-11/20
