Tính nhanh:
( 1 + 1/105 ) x ( 1 + 1/106 ) x ( 1+ 1/107 ) x ( 1+ 1/108 ) x ( 1+ 1/109 )
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\(=\frac{106}{105}\times\frac{107}{106}\times\frac{108}{107}\times\frac{109}{108}\times\frac{110}{109}\)
\(=\frac{110}{105}=\frac{22}{21}\)
(1+1/105)x(1+1/106)x(1+1/107)x(1+1/108)+(1+1/109)
=109/105+110/109
=23431/11445
= 106/105 x 107 / 106 x 108 / 107 x 109/108 x 110/109
= 110/105
=22/21
\(=\frac{106}{105}\times\frac{107}{106}\times...\times\frac{110}{109}\)
\(=\frac{106\times107\times...\times110}{105\times106\times...109}\)
\(=\frac{110}{105}=\frac{22}{21}\)
1,a,\(\left|x+2\right|=x+3\Leftrightarrow\orbr{\begin{cases}x+2=x+3\\x+2=-x-3\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x-x=3-2\\x+x=-3-2\end{cases}\Leftrightarrow\orbr{\begin{cases}0=1\left(voly\right)\\x=\frac{-5}{2}\end{cases}}}\)
b, \(|x-2|=2-x\Leftrightarrow\orbr{\begin{cases}x-2=2-x\\x-2=x-2\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x+x=2+2\\x-x=-2+2\end{cases}\Rightarrow x=2}\)
c,\(\left|2x-1\right|=3\Leftrightarrow\orbr{\begin{cases}2x-1=3\\2x-1=-3\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}2x=4\\2x=-2\end{cases}\Leftrightarrow\orbr{\begin{cases}x=2\\x=-1\end{cases}}}\)
d,\(\left|x-12\right|=x\Leftrightarrow\orbr{\begin{cases}x-12=x\\x-12=-x\end{cases}\Leftrightarrow\orbr{\begin{cases}0=12\left(voly\right)\\x=6\end{cases}}}\)
=101-102-103+104-105-106+107-108+109+110
= (101+104+107+109+110)-(102+103+105+106+108)
=701-704
=-3
a: =(-1)+(-1)+(-1)+(-1)-109=-113
b: =a-1-a+3=2
c: =b+2-b-1=1
\(=\frac{106}{105}.\frac{107}{106}.\frac{108}{107}.\frac{109}{108}.\frac{110}{109}\)
\(=\frac{106.107.108.109.110}{105.106.107.108.109}\)
\(=\frac{110}{105}=\frac{22}{21}.\)