giá trị ngịch dảo của biểu thức
\(2+\frac{1}{2+\frac{1}{2+\frac{1}{2 +\frac{1}{2}}}}\)
trình bày rõ ràng dễ hiểu nhất mình kích
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Đặt \(A=\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{21.22}\)
\(A=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{21}-\frac{1}{22}\)
\(A=\frac{1}{5}-\frac{1}{22}\)
\(A=\frac{17}{110}\)
\(\frac{1}{5.6}\)+\(\frac{1}{6.7}\)+...+\(\frac{1}{21.22}\)
=\(\frac{1}{5}\)-\(\frac{1}{6}\)+\(\frac{1}{6}\)-\(\frac{1}{7}\)+...+\(\frac{1}{21}\)-\(\frac{1}{22}\)
=\(\frac{1}{5}\)-\(\frac{1}{22}\)
=\(\frac{17}{110}\)
Đặt biểu thức là A, ta có:
\(\frac{1}{7}A=\frac{5}{2.7}+\frac{4}{7.11}+\frac{2}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}\)
\(\frac{1}{7}A=\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{15}-\frac{1}{28}\)
1/7 A = 1/2 - 1/28
1/7A = 17/28
=> A = 17/4
\(A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{99}}+\frac{1}{2^{100}}+\frac{1}{2^{100}}\)
=>\(2A=2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{98}}+\frac{1}{2^{99}}+\frac{1}{2^{99}}\)
=>\(A=2A-A=2+\frac{1}{2^{99}}+\frac{1}{2^{99}}\)
\(A=2+\frac{1}{2^{98}}\)
Vậy: \(A=2+\frac{1}{2^{98}}\)
Gọi \(B=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{100}}\)
\(\Rightarrow2B=2+1+\frac{1}{2}+...+\frac{1}{2^{99}}\)
\(\Rightarrow2B-B=\left(2+1+\frac{1}{2}+...+\frac{1}{2^{99}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{100}}\right)\)
\(\Rightarrow B=2-\frac{1}{2^{100}}\)
\(\Rightarrow A=2\)
Vậy A = 2
Ta có:
1/2^2+1/3^2+.....+1/20^2>1/2.2+1/3.4+1/4.5+.....+1/20.21
=1/4+1/3-1/21
=1/4+6/21
=45/84>1/2
Ta có:
1/2^2+1/3^2+..........+1/20^2<1/1.2+1/2.3+.....+1/19.20
=1-1/20
=19/20<1
a,
\(\Leftrightarrow A=\left(\frac{x+1}{\left(x+1\right)\left(x-1\right)}+\frac{x}{\left(x+1\right)\left(x-1\right)}\right):\frac{2x+1}{\left(x+1\right)^2}\)
\(\Leftrightarrow A=\frac{2x+1}{\left(x+1\right)\left(x-1\right)}\cdot\frac{\left(x+1\right)^2}{2x+1}\)
\(\Leftrightarrow A=\frac{x+1}{x-1}\)
b, dùng máy tính kq là-3