\(\Leftrightarrow A=\frac{1}{2}+\frac{1}{2\cdot7}+\frac{1}{7.5}+\frac{1}{5.13}+\frac{1}{13.8}+\frac{1}{8.19}\)
\(\Rightarrow A=\frac{1}{2}+\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{5}+\frac{1}{5}-\frac{1}{13}+\frac{1}{13}-\frac{1}{8}+\frac{1}{8}-\frac{1}{19}\)
\(\Rightarrow A=-\frac{1}{19}\)
Tính giá trị biểu thức A , biết rằng A = M : N
Mà M = \(\dfrac{\dfrac{1}{99}+\dfrac{2}{98}+\dfrac{3}{97}+\dfrac{4}{96}+...+\dfrac{97}{3}+\dfrac{98}{2}+\dfrac{99}{1}}{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}+...+\dfrac{1}{100}}\)
N = \(\dfrac{92-\dfrac{1}{9}-\dfrac{2}{10}-\dfrac{3}{11}-...-\dfrac{90}{98}-\dfrac{91}{99}-\dfrac{92}{100}}{\dfrac{1}{45}+\dfrac{1}{50}+\dfrac{1}{55}+...+\dfrac{1}{495}+\dfrac{1}{500}}\)
Cho \(\dfrac{a+b+c-d}{d}\)=\(\dfrac{b+c+d-a}{a}\)=\(\dfrac{c+d+a-b}{b}\)=\(\dfrac{d+a+b-c}{c}\), (a+b+c+d) khác 0
tính giá trị của biểu thức: P=(1+\(\dfrac{b+c}{a}\))(1+\(\dfrac{c+d}{b}\))(1+\(\dfrac{d+a}{c}\))(1+\(\dfrac{a+b}{d}\))
Cho 3 số x,y,z khác 0 thoả mãn điều kiện \(\dfrac{y+z-x}{x}=\dfrac{z+x-y}{y}=\dfrac{x+y-z}{z}\)
Hãy tính giá trị của biểu thức :
\(B=\left(1+\dfrac{x}{y}\right)\left(1+\dfrac{y}{z}\right)\left(1+\dfrac{z}{x}\right)\)
Bài 1Tính giá trị biểu thức:
C=\(\dfrac{9}{10}-\dfrac{1}{90}-\dfrac{1}{72}-\dfrac{1}{56}-\dfrac{1}{42}-\dfrac{1}{30}-\dfrac{1}{20}-\dfrac{1}{12}-\dfrac{1}{6}-\dfrac{1}{2}\)
Tính giá trị biểu thức : \(A=\dfrac{\left(\dfrac{1}{2}\right)^2.2018-\left(\dfrac{1}{4}\right)^6.2017}{\dfrac{1}{4096}.\dfrac{1}{3}-\left(\dfrac{1}{2}\right)^{13}}\)
tính giá trị của biểu thức : B\(=\dfrac{\left(\dfrac{1}{2}\right)^{10}.5-\left(\dfrac{1}{4}\right)^5.3}{\dfrac{1}{1024}.\dfrac{1}{3}-\left(\dfrac{1}{2}\right)^{11}}\)
Bài 17: Cho a, b, c là 3 số thực khác 0, thỏa mãn điều kiện : \(a+b\ne-c\) và \(\dfrac{a+b-c}{c}\)=\(\dfrac{b+c-a}{a}\)=\(\dfrac{c+a-b}{b}\). Tính giá trị biểu thức P=\(\left(1+\dfrac{b}{a}\right)\)x\(\left(1+\dfrac{a}{c}\right)\)x\(\left(1+\dfrac{c}{b}\right)\)
Tinh
\(\dfrac{\left(1+2+3+...+100\right)\left(\dfrac{1}{3}-\dfrac{1}{5}-\dfrac{1}{7}-\dfrac{1}{9}\right)\left(6,3.12-21.36\right)}{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{100}}\)
\(\dfrac{\left(\dfrac{3}{10}-\dfrac{4}{15}-\dfrac{7}{20}\right).\dfrac{5}{9}}{\left(\dfrac{1}{14}+\dfrac{1}{7}-\dfrac{-3}{35}\right)\dfrac{-4}{3}}\)
Tính giá trị biểu thức:
\(D=\dfrac{\dfrac{1}{2003}+\dfrac{1}{2004}+\dfrac{1}{2005}}{\dfrac{5}{2003}+\dfrac{5}{2004}+\dfrac{5}{2005}}-\dfrac{\dfrac{2}{2002}+\dfrac{2}{2003}+\dfrac{2}{2004}}{\dfrac{2}{2002}+\dfrac{3}{2003}+\dfrac{3}{2004}}\)
\(H=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2012}}{\dfrac{2011}{1}+\dfrac{2010}{2}+...+\dfrac{1}{2011}}\)
\(I=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2012}}{\dfrac{2012}{2}+\dfrac{2012}{3}+...+\dfrac{2012}{2011}}\)
Help me!
