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a. -3/4 x 12/-5 x (-25/6)=-15/2
b. -2 x -38/21 x -7/4 x (-3/8)=-19/8
c. (11/12: 33/16) x 3/5=4/15
d. 7/23 x [(-8/6)- 45/18]=-7/6
\(a,=\left(\frac{15}{12}-\frac{3}{12}\right)+\left(\frac{5}{13}-\frac{18}{13}\right)\)
\(=1+-1\)
\(=0\)
Lời giải:
$A=1-3+3^2-3^3+3^4-....+3^{38}-3^{39}$
$3A=3-3^2+3^3-3^4+3^5-...+3^{39}-3^{40}$
$A+3A=(1-3+3^2-3^3+3^4-....+3^{38}-3^{39})+(3-3^2+3^3-3^4+3^5-...+3^{39}-3^{40})$
$4A=1-3^{40}$
b.
Xét $B=1-3+3^2-3^3+....+3^{98}-3^{99}$
$3B=3-3^2+3^3-3^4+....+3^{99}-3^{100}$
$\Rightarrow B+3B=1-3^{100}$
$4B=1-3^{100}$
$3^{100}=1-4B$
Suy ra $3^{100}$ chia $4$ dư $1$
\(a.=\frac{3}{15}+\frac{-10}{15}\)
\(=-\frac{7}{15}\)
\(b.=\left(\frac{15}{12}-\frac{3}{12}\right)+\left(\frac{5}{13}-\frac{18}{13}\right)\)
\(=1+\left(-1\right)\)
\(=0\)
\(c.=\left(\frac{13}{25}-\frac{38}{25}\right)+\left(\frac{6}{41}+\frac{35}{41}\right)-\frac{1}{2}\)
\(=-1+1-\frac{1}{2}\)
\(=0-\frac{1}{2}\)
\(=-\frac{1}{2}\)
\(d.=\frac{5}{6}.\left(18\frac{2}{3}-6\frac{2}{3}\right)\)
\(=\frac{5}{6}.12\)
\(=10\)
`Answer:`
\(A+B=\left(6x^3+2y^3-y-1\right)+\left(5x^4-2y^3+3x^2-5y+1\right)\)
\(=5x^4+6x^3+\left(2y^3-2y^3\right)+3x^2+\left(-y-5y\right)+\left(-1+1\right)\)
\(=5x^4+6x^3+3x^2-6y\)
\(A+B=\left(6x^3+2y^3-y-1\right)+\left(5x^4-2y^3+3x^2-5y+1\right)\)
\(=6x^3+2y^3-y-1+5x^4-2y^3+3x^2-5y+1\)
\(=6x^3+\left(2y^3-2y^3\right)+\left(-y-5y\right)+\left(-1+1\right)+5x^4+3x^2\)
\(=6x^3+\left(-6\right)y+5x^4+3x^2\)
\(=6x^3-6y+5^4+3x^2\)
a = 2,(12) + 3,(38)
a = 2 + 0,(12) + 3 + 0,(38)
a = 5 + 0,(50)
a = 5 + 0,(01).50
\(a=5+\frac{1}{99}.50\)
\(a=5+\frac{50}{99}=\frac{545}{99}\)