10.50+20.23 = ?
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(20,23:0,5+20,23:0,25+20,23\times94\)
\(=20,23\times2+20,23\times4+20,23\times94\)
\(=20,23\times\left(2+4+94\right)=20,23\times100=2023\)
![](https://rs.olm.vn/images/avt/0.png?1311)
=1/3.(3/14.17+3/17.20+...+3/161.164)
=1/3.(1/14-1/17+1/17-1/20+...+1/161-1/164)
=1/3.(1/14-1/164)
=1/3.75/1148
=25/1148
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có \(\dfrac{1}{20.23}+\dfrac{1}{23.26}+...+\dfrac{1}{77.80}=\dfrac{1}{3}\left(\dfrac{1}{20}-\dfrac{1}{23}+\dfrac{1}{23}-\dfrac{1}{26}+...+\dfrac{1}{77}-\dfrac{1}{80}\right)=\dfrac{1}{3}\left(\dfrac{1}{20}-\dfrac{1}{80}\right)=\dfrac{1}{3}.\dfrac{3}{80}=\dfrac{1}{80}< \dfrac{1}{9}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{20.23} +\frac{1}{23.26}+\frac{1}{26.29}+...+\frac{1}{77.80}\)
= \(\frac{1}{3}.\left(\frac{3}{20.23}+\frac{3}{23.26}+\frac{3}{26.29}+...+\frac{3}{77.80}\right)\)
= \(\frac{1}{3}.\left(\frac{1}{20}-\frac{1}{23}+\frac{1}{23}-\frac{1}{26}+\frac{1}{26}-\frac{1}{29}+...+\frac{1}{77}-\frac{1}{80}\right)\)
= \(\frac{1}{3}.\left(\frac{1}{20}-\frac{1}{80}\right)\)
= \(\frac{1}{3}.\frac{3}{80}\)
= \(\frac{1}{80}\) < \(\frac{1}{9}\)
⇒ \(\frac{1}{20.23} +\frac{1}{23.26}+\frac{1}{26.29}+...+\frac{1}{77.80}\) < \(\frac{1}{9}\) (ĐPCM)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{20.23}+\frac{1}{23.26}+...+\frac{1}{77.80} \)
\(=\frac{1}{3}.(\frac{1}{20}-\frac{1}{23})+\frac{1}{3}.(\frac{1}{23}-\frac{1}{26})+...+\frac{1}{3}.(\frac{1}{77}-\frac{1}{80})\)
=\(\frac{1}{3}.(\frac{1}{20}-\frac{1}{23}+\frac{1}{23}-\frac{1}{26}+...+\frac{1}{77}-\frac{1}{80})\)
=\(\frac{1}{3}.(\frac{1}{20}-\frac{1}{80})\)
=\(\frac{1}{3}.\frac{3}{80}\)
=\(\frac{1}{80}\)<\(\frac{1}{9}\)
Vậy tổng trên nhỏ hơn \(\frac{1}{9}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
E=1/1.3+1/3.6+1/6.9+.............+1/20.23
<=>E=1/1-1/3+1/3-1/6+1/6-1/9+...........+1/20-1/23
<=>E=1/1-1/23
<=>E=22/23
Kb và k mk nha mn.
Cho hai phan so 1/n va 1/n+1 (n thuoc z)chung to rang h cua hai phan so nay bang hieu cua chung
10.50+20.23=960