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\(M=\frac{13}{12}+\frac{21}{20}+\frac{31}{30}+\frac{43}{42}+\frac{57}{56}+\frac{73}{72}\)
\(\Rightarrow M=\left(1+\frac{1}{12}\right)+\left(1+\frac{1}{20}\right)+\left(1+\frac{1}{30}\right)+\left(1+\frac{1}{42}\right)+\left(1+\frac{1}{56}\right)+\left(1+\frac{1}{72}\right)\)
\(\Rightarrow M=6+\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)\)
\(\Rightarrow M=6+\left(\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}\right)\)
\(\Rightarrow M=6+\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{8}-\frac{1}{9}\right)\)
\(\Rightarrow M=6+\left(\frac{1}{3}-\frac{1}{9}\right)=6+\left(\frac{3}{9}-\frac{1}{9}\right)\)
\(\Rightarrow M=6+\frac{2}{9}=\frac{54}{9}+\frac{2}{9}=\frac{56}{9}\)
a) \(21^{15}=21^{3.5}=\left(21^3\right)^5=9261^5\)
Vì \(9261>27\Rightarrow9261^5>27^5\Rightarrow21^{15}>27^5\)
b) \(15^{12}=\left(3.5\right)^{12}=3^{12}.5^{12}\)
\(81^3.125^5=\left(3^4\right)^3.\left(5^3\right)^5=3^{4.3}.5^{3.5}=3^{12}.5^{15}\)
Vì \(3^{12}=3^{12}\)mà \(5^{12}< 5^{15}\Rightarrow3^{12}.5^{12}< 3^{12}.5^{15}\Rightarrow15^{12}< 81^3.125^5\)
Nguyễn Hoàng Thiên Di
tính thường cx đc mà tính nhanh càng tốt nha
1/ -7264 + (1543 + 7264)
=-7264 + 1543 + 7264=1543
2/ (144 – 97) – 144
=144-97-144=-97
3/ (-145) – (18 – 145)(Vì có dấu trừ ở trước ngoặc nên p đổi dấu)
=-145-18+145=-18
4/ 111 + (-11 + 27)
=111-11+27=137
\(\left|-34\right|+(-4)\cdot(-1)^{2008}+(17-19)^2\)
\(=34+4+(-2)^2\)
\(=34+4+4\)
\(=42\)
\((-31)\cdot81-18\cdot31-31\)
\(=31\cdot(-81)-18\cdot31-31\)
\(=31\cdot(-81)-18-1\)
\(=31\cdot(-100)=-3100\)
1. \(\left(387-41\right)-\left(81+13\right)\)
\(=346-94=252\)
2. \(\left(83+81\right)-\left(81+13\right)\)
\(=83+81-81-13\)
\(=70\)
3. \(281-\left(-37\right)+83-181\)
\(=281-181+37+83\)
\(=100+120=220\)
4. \(87-\left(-13\right)+\left(-21\right)-79\)
\(=87+13-21-79\)
\(=100-100=0\)
5. \(\left(-172\right)+\left(-43\right)+72-57\)
\(=-172+72-43-57\)
\(=-100-100=-200\)
b: =83+81-81-13=70
2: =281+37+83-181=100+120=220