10.50+20.23=960

=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

Ta có \(\dfrac{1}{20.23}+\dfrac{1}{23.26}+...+\dfrac{1}{77.80}=\dfrac{1}{3}\left(\dfrac{1}{20}-\dfrac{1}{23}+\dfrac{1}{23}-\dfrac{1}{26}+...+\dfrac{1}{77}-\dfrac{1}{80}\right)=\dfrac{1}{3}\left(\dfrac{1}{20}-\dfrac{1}{80}\right)=\dfrac{1}{3}.\dfrac{3}{80}=\dfrac{1}{80}< \dfrac{1}{9}\)

Ta có:

\(\dfrac{1}{20.23}+\dfrac{1}{23.26}+\dfrac{1}{26.29}+...+\dfrac{1}{77.80}\)

=\(\dfrac{1}{3}\left[\left(\dfrac{1}{20}-\dfrac{1}{23}\right)+\left(\dfrac{1}{23}-\dfrac{1}{26}\right)+\left(\dfrac{1}{26}-\dfrac{1}{29}\right)+...+\left(\dfrac{1}{77}-\dfrac{1}{80}\right)\right]\)

= \(\dfrac{1}{3}\left(\dfrac{1}{20}-\dfrac{1}{80}\right)\)

=\(\dfrac{1}{3}.\dfrac{3}{80}\)

=\(\dfrac{1}{80}\)

Vì \(\dfrac{1}{80}\)>\(\dfrac{1}{9}\)

Nên \(\dfrac{1}{20.23}+\dfrac{1}{23.26}+\dfrac{1}{26.29}+...+\dfrac{1}{77.80}>\dfrac{1}{9}\)

Ta có:

\(\\ \dfrac{1}{20.23}+\dfrac{1}{23.26}+...+\dfrac{1}{77.80}\\ =\dfrac{1}{3}\left(\dfrac{1}{20}-\dfrac{1}{23}+\dfrac{1}{23}-\dfrac{1}{26}+...+\dfrac{1}{77}-\dfrac{1}{80}\right)\\ =\dfrac{1}{3}\left(\dfrac{1}{20}-\dfrac{1}{80}\right)\\ =\dfrac{1}{3}\left(\dfrac{3}{80}-\dfrac{1}{80}\right)\\ =\dfrac{1}{3}.\dfrac{3}{80}\\ =\dfrac{1}{80}\\ \)

Vậy \(\dfrac{1}{80}< \dfrac{1}{9}\)

\(\frac{1}{20.23} +\frac{1}{23.26}+\frac{1}{26.29}+...+\frac{1}{77.80}\)

= \(\frac{1}{3}.\left(\frac{3}{20.23}+\frac{3}{23.26}+\frac{3}{26.29}+...+\frac{3}{77.80}\right)\)

= \(\frac{1}{3}.\left(\frac{1}{20}-\frac{1}{23}+\frac{1}{23}-\frac{1}{26}+\frac{1}{26}-\frac{1}{29}+...+\frac{1}{77}-\frac{1}{80}\right)\)

= \(\frac{1}{3}.\left(\frac{1}{20}-\frac{1}{80}\right)\)

= \(\frac{1}{3}.\frac{3}{80}\)

= \(\frac{1}{80}\) < \(\frac{1}{9}\)

⇒ \(\frac{1}{20.23} +\frac{1}{23.26}+\frac{1}{26.29}+...+\frac{1}{77.80}\) < \(\frac{1}{9}\) (ĐPCM)

cần lắm đúng ko

(23.20+3)46:2=10649

\(\frac{1}{20.23}+\frac{1}{23.26}+...+\frac{1}{77.80} \)

\(=\frac{1}{3}.(\frac{1}{20}-\frac{1}{23})+\frac{1}{3}.(\frac{1}{23}-\frac{1}{26})+...+\frac{1}{3}.(\frac{1}{77}-\frac{1}{80})\)

=\(\frac{1}{3}.(\frac{1}{20}-\frac{1}{23}+\frac{1}{23}-\frac{1}{26}+...+\frac{1}{77}-\frac{1}{80})\)

=\(\frac{1}{3}.(\frac{1}{20}-\frac{1}{80})\)

=\(\frac{1}{3}.\frac{3}{80}\)

=\(\frac{1}{80}\)<\(\frac{1}{9}\)

Vậy tổng trên nhỏ hơn \(\frac{1}{9}\)

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