Tinhs pheps tinhs sau :
B = \(-\dfrac{3}{5}+\dfrac{28.43}{5.56}+\dfrac{28.5}{5.24}-\dfrac{28.21}{5.63}\)
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\(\frac{-3}{5}+\frac{28.43}{5.56}+\frac{28.5}{5.24}-\frac{28.21}{5.63}\)
=\(\frac{-3}{5}+\frac{2.2.7.43}{5.2.2.7.2}+\frac{2.2.7.5}{2.2.2.3.5}-\frac{2.2.7.3.7}{5.7.3.3}\)
=\(\frac{-3}{5}+\frac{43}{5.2}+\frac{7}{2.3}-\frac{28}{15}\)
=\(\frac{-3}{5}+\frac{43}{10}+\frac{7}{6}-\frac{28}{15}\)
=\(\frac{-18}{30}+\frac{129}{30}+\frac{35}{30}-\frac{56}{30}\)
=\(\frac{-18+129+35-56}{30}\)
=\(\frac{90}{30}=3\)
Chúc bn học tốt
b
.ta có
=-3/5+28/5.43/56+28/5.5/24-28/5.21/63
=-3/5+28/5.(43/56+5/24-21/63)
=5.9/14=45/14
suy ra
biểu thức b có giá trị là 45/14
-3/5 + 28.43/5.56 + 28.5/5.24 - 28.21/5.63
=-3/5 + 28.43/5.28.2 + 4.7.5/5.4.6 - 28.21/5.3.21
=-3/5 + 43/10 + 7/6 - 28/15
=-18/30 + 129/30 + 35/30 - 56/30
=-12+129+35-56/30
=94/30=47/15
\(\dfrac{1}{1}+\dfrac{1}{3}+\dfrac{1}{9}+...+\dfrac{1}{729}\\ =\dfrac{1}{1}+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^6}\\ =\dfrac{3-1}{2}\cdot\left(\dfrac{1}{1}+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^6}\right)\\ =\dfrac{\left(3-1\right)\left(\dfrac{1}{1}+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^6}\right)}{2}\\ =\dfrac{3-1+1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{3^2}+...+\dfrac{1}{3^5}-\dfrac{1}{3^6}}{2}\\ =\dfrac{3-\dfrac{1}{3^6}}{2}\\ =\dfrac{\dfrac{3^7}{3^6}-\dfrac{1}{3^6}}{2}\\ =\dfrac{2187-1}{729}\cdot\dfrac{1}{2}\\ =\dfrac{2186}{729}\cdot\dfrac{1}{2}\\ =\dfrac{1093}{729}\)
Đặt biểu thức là P , theo bài ra ta có:
\(\dfrac{1}{3}P=\dfrac{1}{3}+\dfrac{1}{3^2}+.......+\dfrac{1}{3^6}+\dfrac{1}{3^7}\)
\(=>P-\dfrac{1}{3}P=\left(1-\dfrac{1}{3^7}\right)\)
\(=>\dfrac{2}{3}P=\dfrac{2186}{2187}\)
\(=>P=\dfrac{2186}{2187}:\dfrac{2}{3}=\dfrac{1093}{729}\)
CHÚC BẠN HỌC TỐT.......
\(\dfrac{1}{x^2+x+1}-\dfrac{1}{x-x^2}-\dfrac{x^2+2x}{x^3-1}\)
\(=\dfrac{\left(x-1\right)x}{x\left(x-1\right)\left(x^2+x+1\right)}+\dfrac{x^2+x+1}{x\left(x-1\right)\left(x^2+x+1\right)}-\dfrac{\left(x^2+2x\right)x}{x\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{x^2-x+x^2+x+1-x^3-2x^2}{x\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{1-x^3}{x\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{-\left(x^3-1\right)}{x\left(x^3-1\right)}=\dfrac{-1}{x}\)
\(\dfrac{-3}{5}+\dfrac{43}{10}+\dfrac{7}{6}-\dfrac{28}{15}\)
\(=3\)