BT6 : Cho A = 124 . ( 1/1.1985 + 1/2.1986 + 1/3.1987 +......+1/16.200 )
B = 1/1.17 + 1/20.18 +....+1/1984.2000
So sánh A và B
BT7: Cho P = 12/1.4.7 + 12/4.7.10 + 12/7.10.13 +....+12/54.57.60
So sánh P và 1/2
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so sánh : A = \(124.\left(\frac{1}{1.1985}+\frac{1}{2.1986}+\frac{1}{3.1987}+...+\frac{1}{16.2000}\right)\)
B=\(\frac{1}{1.17}+\frac{1}{2.18}+\frac{1}{3.19}+...+\frac{1}{1984.2000}\)
\(A=124\left(\frac{1}{1.1985}+\frac{1}{2.1986}+\frac{1}{3.1987}+...+\frac{1}{16.2000}\right)\)
\(=\frac{124}{1984}.\left(1-\frac{1}{1985}+\frac{1}{2}-\frac{1}{1986}+...+\frac{1}{16}-\frac{1}{2000}\right)\)
\(=\frac{1}{16}\left[\left(1+\frac{1}{2}+...+\frac{1}{16}\right)-\left(\frac{1}{1985}+\frac{1}{1986}+...+\frac{1}{2000}\right)\right]\)
Và \(B=\frac{1}{1.17}+\frac{1}{2.18}+...+\frac{1}{1984.2000}\)
\(=\frac{1}{16}\left[\left(1-\frac{1}{17}+\frac{1}{2}-\frac{1}{18}+...+\frac{1}{1984}-\frac{1}{2000}\right)\right]\)
\(=\frac{1}{16}\left[\left(1+\frac{1}{2}+...+\frac{1}{1984}\right)-\left(\frac{1}{17}+\frac{1}{18}+...+\frac{1}{2000}\right)\right]\)
= \(\frac{1}{16}\) . \(\left[\left(1+...+\frac{1}{16}\right)+\left(\frac{1}{17}+...+\frac{1}{1984}-\frac{1}{17}-...-\frac{1}{1984}\right)-\left(\frac{1}{1985}+...+\frac{1}{2000}\right)\right]\)
= \(=\frac{1}{16}\left[\left(1+\frac{1}{2}+...+\frac{1}{16}\right)-\left(\frac{1}{1985}+\frac{1}{1986}+...+\frac{1}{2000}\right)\right]\)
Vậy A = B
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So sánh 2 biểu thức:
\(A=124\left(\frac{1}{1.1985}+\frac{1}{2.1986}+\frac{1}{3.1987}+...+\frac{1}{16.2000}\right)\)
\(B=\frac{1}{1.17}+\frac{1}{2.18}+\frac{1}{3.19}+...+\frac{1}{1984.2000}\)
So sánh A và B biết :
A = 124.(1/1.1985 + 1/2.1986 + ... + 1/16.2000
B = 1/1.17 + 1/2.18 + 1/3.19 + ... + 1/1984.2000
`Answer:`
\(A=124.\left(\frac{1}{1.1985}+\frac{1}{2.1986}+\frac{1}{3.1987}+...+\frac{1}{16.2000}\right)\)
\(=\frac{124}{1984}.\left(\frac{1984}{1.1985}+\frac{1984}{2.1986}+\frac{1984}{3.1987}+...+\frac{1984}{16.2000}\right)\)
\(=\frac{1}{16}.\left(1-\frac{1}{1985}+\frac{1}{2}-\frac{1}{1986}+\frac{1}{3}-\frac{1}{1987}+...+\frac{1}{16}-\frac{1}{2000}\right)\)
\(=\frac{1}{16}.\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{16}\right)\left(\frac{1}{1985}+\frac{1}{1986}+\frac{1}{1987}+...+\frac{1}{2000}\right)\)
\(B=\frac{1}{1.17}+\frac{1}{2.18}+...+\frac{1}{1984.2000}\)
\(=\frac{1}{16}.\left(\frac{16}{1.17}+\frac{16}{2.18}+...+\frac{16}{1984.2000}\right)\)
\(=\frac{1}{16}.\left(1-\frac{1}{17}+\frac{1}{2}-\frac{1}{18}+...+\frac{1}{1984}-\frac{1}{2000}\right)\)
\(=\frac{1}{16}.\left(1-\frac{1}{17}+\frac{1}{2}-\frac{1}{18}+...+\frac{1}{1984}-\frac{1}{2000}\right)\)
\(=\frac{1}{16}.\left(1+\frac{1}{2}+...+\frac{1}{16}\right)+\left(\frac{1}{17}+\frac{1}{18}+...+\frac{1}{1984}\right)-\left(\frac{1}{17}+\frac{1}{18}+...+\frac{1}{1984}\right)-\left(\frac{1}{1985}+\frac{1}{1986}+...+\frac{1}{2000}\right)\)
\(=\frac{1}{16}.[\left(1+\frac{1}{2}+...+\frac{1}{16}\right)-\left(\frac{1}{1985}+\frac{1}{1986}+...+\frac{1}{2000}\right)]\)
`=>A=B`
So sánh A và B biết:
\(a=124.\left(\frac{1}{1.1985}+\frac{1}{2.1986}+\frac{1}{3.1987}+...+\frac{1}{16.2000}\right)\)
\(b=\frac{1}{1.17}+\frac{1}{2.18}+\frac{1}{3.19}+...+\frac{1}{1984.2000}\)
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So sánh 2 biểu thức:
A = 124.\(\left(\frac{1}{1.1985}+\frac{1}{2.1986}+\frac{1}{3.1987}+.....+\frac{1}{16.2000}\right)\)
B = \(\frac{1}{1.17}+\frac{1}{2.18}+\frac{1}{3.19}+......+\frac{1}{1984.2000}\)
So sánh 2 biểu thức:
\(A=124.\left(\frac{1}{1.1985}+\frac{1}{2.1986}+\frac{1}{3.1987}+...+\frac{1}{16.2000}\right)\)
\(B=\frac{1}{1.17}+\frac{1}{2.18}+\frac{1}{3.19}+...+\frac{1}{1984.2000}\)
So sánh A và B
\(A=124.\left(\frac{1}{1.1985}+\frac{1}{2.1986}+\frac{1}{3.1987}+....+\frac{1}{16.2000}\right)\)
\(B=\frac{1}{1.17}+\frac{1}{2.18}+\frac{1}{3.19}+.....+\frac{1}{1984.2000}\)
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Ta có: \(A=124\cdot\frac{1}{1984}\cdot\left(1-\frac{1}{1985}+\frac{1}{2}-\frac{1}{1986}+\frac{1}{3}-\frac{1}{1987}+...+\frac{1}{16}-\frac{1}{2000}\right)\)
\(\Rightarrow A=\frac{1}{16}\cdot\left[\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{16}\right)-\left(\frac{1}{1985}+\frac{1}{1986}+\frac{1}{1987}+...+\frac{1}{2000}\right)\right]\)
Laji cos: \(B=\frac{1}{16}\cdot\left(1-\frac{1}{17}+\frac{1}{2}-\frac{1}{18}+\frac{1}{3}-\frac{1}{19}+...+\frac{1}{1984}-\frac{1}{2000}\right)\)
\(\Rightarrow B=\frac{1}{16}\cdot\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{1984}-\frac{1}{17}-\frac{1}{18}-\frac{1}{19}-...-\frac{1}{2000}\right)\)
\(\Rightarrow B=\frac{1}{16}\cdot\left[\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{1984}\right)-\left(\frac{1}{17}+\frac{1}{18}+\frac{1}{19}+...+\frac{1}{2000}\right)\right]\)
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So sánh
A=124.\(\left(\frac{1}{1.1985}+\frac{1}{2.1986}+\frac{1}{3.1987}+...+\frac{1}{16.2000}\right)\)
Và B=\(\frac{1}{1.17}+\frac{1}{2.18}+\frac{1}{3.19}+...+\frac{1}{1984.2000}\)
A= 124.[1/1.1985+1/2.1986+/3.1987+...+1/16.2000]
B= 1/1.17+1/2.18+...+1/1984.2000
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