Cho \
M=1/10+1/15+1/21+1/28+...1/105+1/120
Chứng tỏ rằng 1/3<M<1/2
Gợi ý nha: M=2x[1/4x5+1/5x6+1/6x7+...1/15x16]
giúp mình nha!!!!!
Cho M= \(\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}+\dfrac{1}{28}+...+\dfrac{1}{105}+\dfrac{1}{120}\). Chứng minh rằng: \(\dfrac{1}{3}< M< \dfrac{1}{2}\)
\(M=\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}+...+\dfrac{1}{105}+\dfrac{1}{120}\)
\(M=2.\left(\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+...+\dfrac{1}{240}\right)\)
\(M=2.\left(\dfrac{1}{4.5}+\dfrac{1}{5.6}+...+\dfrac{1}{15.16}\right)\)
\(M=2.\left(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{15}-\dfrac{1}{16}\right)\)
\(M=2.\left(\dfrac{1}{4}-\dfrac{1}{16}\right)\)
\(M=2.\dfrac{3}{16}\)
\(M=\dfrac{3}{8}\)
Vậy \(\dfrac{1}{3}< M< \dfrac{1}{2}\)
cho M = 1/10 + 1/15 + 1/21 + 1/28 + ....+ 1/105 + 1 /120.Chung to 1/3 < M < 1/2
\(M=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+...+\frac{1}{105}+\frac{1}{120}\)
\(M=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+...+\frac{2}{210}+\frac{2}{240}\)
\(M=\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+\frac{2}{7.8}+...+\frac{2}{14.15}+\frac{2}{15.16}\)
\(M=\frac{2}{4}-\frac{2}{5}+\frac{2}{5}-\frac{2}{6}+\frac{2}{6}-\frac{2}{7}+\frac{2}{7}-\frac{2}{8}+...+\frac{2}{15}-\frac{2}{16}\)
\(M=\frac{2}{4}-\frac{2}{16}=\frac{3}{8}\)
Vì \(\frac{3}{9}< \frac{3}{8}< \frac{4}{8}\)nên \(\frac{1}{3}< M< \frac{1}{2}\)
Vậy \(\frac{1}{3}< M< \frac{1}{2}\)
P/S : Đừng nói như lần trước nhé!
Chứng tỏ rằng: 1/10+1/15+1/21+1/28+1/36+1/45=3/10
thì cộng vào nó vẫn ra 3/10 mà
BẠN BÀO GIÚP MÌNH VỚI
Cho M= \(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+....+\frac{1}{105}+\frac{1}{120}\)
Chứng tỏ \(\frac{1}{3}< M< \frac{1}{2}\)
CÁC BẠN GIẢI ĐẦY ĐỦ HỘ MÌNH NHÉ
M=1/10 + 1/15 + 1/21 +....+ 1/120
M=2/20 +2/30+2/42+....+2/240
M=2/4.5 + 2/5.6 + 2/6.7 +.....+ 2/15.16
M=2.(1/4.5 +......+ 1/15.16)
M=2.(1/4 -1/5 +1/5 - 1/6 +.....+ 1/15 - 1/16)
M=2.(1/4 - 1/16)
M=2.(4/16 - 1/16)
M=2. 3/16
M=6/16=3/8
Có 1/3 = 8/24 < 9/24 = 3/8 =>1/3<M
Có 1/2 = 4/8>3/8 =>1/2 >M
=> 1/3 < M < 1/2
Cho M=\(\frac{1}{10}\)+\(\frac{1}{15}\)+\(\frac{1}{21}\)+\(\frac{1}{28}\)+...........+\(\frac{1}{105}\)+\(\frac{1}{120}\). Chứng tỏ \(\frac{1}{3}\)<M<\(\frac{1}{2}\)
Cho M=\(\frac{1}{10}+\frac{1}{15}+\frac{1}{20}+\frac{1}{28}+...+\frac{1}{105}+\frac{1}{420}\)chứng minh rằng \(\frac{1}{3}< M< \frac{1}{2}\)
tính
a)\(\dfrac{-10}{11}.\dfrac{8}{9}+\dfrac{7}{18}.\dfrac{10}{11}\)
b)\(\dfrac{3}{14}:\dfrac{1}{28}-\dfrac{13}{21}:\dfrac{1}{28}+\dfrac{29}{42}:\dfrac{1}{28}-8\)
c)\(-1\dfrac{5}{7}.15+\dfrac{2}{7}\left(-15\right)+\left(-105\right).\left(\dfrac{2}{3}-\dfrac{4}{5}+\dfrac{1}{7}\right)\)
a)\(\dfrac{-10}{11}.\dfrac{8}{9}+\dfrac{7}{18}.\dfrac{10}{11}\)
=\(\dfrac{10}{11}.\dfrac{-8}{9}+\dfrac{7}{18}.\dfrac{10}{11}\)
=\(\dfrac{10}{11}(\dfrac{-8}{9}+\dfrac{7}{18})\)
=\(\dfrac{10}{11}.\dfrac{-1}{2}\)
=\(\dfrac{-5}{11}\)
b;
B = \(\dfrac{3}{14}\) : \(\dfrac{1}{28}\) - \(\dfrac{13}{21}\): \(\dfrac{1}{28}\) + \(\dfrac{29}{42}\) : \(\dfrac{1}{28}\) - 8
B = (\(\dfrac{3}{14}\) - \(\dfrac{13}{21}\) + \(\dfrac{29}{42}\)) - 8
B = (\(\dfrac{9}{42}\) - \(\dfrac{26}{42}\) + \(\dfrac{29}{42}\)) - 8
B = (\(\dfrac{-17}{42}\) + \(\dfrac{29}{42}\)) - 8
B = \(\dfrac{2}{7}\) - 8
B = \(\dfrac{2}{7}-\dfrac{56}{7}\)
B = - \(\dfrac{54}{7}\)
c; C = -1\(\dfrac{5}{7}\).15 + \(\dfrac{2}{7}\)(-15) + (-105).(\(\dfrac{2}{3}\) - \(\dfrac{4}{5}\) + \(\dfrac{1}{7}\))
C = - 15.(- 1 - \(\dfrac{5}{7}\) + \(\dfrac{2}{7}\) + \(\dfrac{14}{3}\) - \(\dfrac{28}{5}\) + \(1\))
C = -15.[(1 - 1) - (\(\dfrac{5}{7}\) - \(\dfrac{2}{7}\)) + \(\dfrac{14}{3}\) - \(\dfrac{28}{5}\)]
C = -15.[0 - \(\dfrac{3}{7}\) + \(\dfrac{14}{3}\) - \(\dfrac{28}{5}\)]
C = -15 . [- \(\dfrac{45}{105}\) + \(\dfrac{490}{105}\) - \(\dfrac{588}{105}\)]
C = -15. [ \(\dfrac{445}{105}\) - \(\dfrac{588}{105}\)]
C = - 15.(- \(\dfrac{143}{105}\))
C = \(\dfrac{143}{7}\)
Tính:a,(-40/41.0,32.17/20):64/75
b,-10/11.8/9+7/18.10/11
c,3/14:1/28-13/21:1/28+29/42:1/28-8
d,-12/7.15+2/7.(-15)+(-105).(2/3-4/5+1/7)
TÌM X BIẾT :
x/2017-1/10-1/15-1/21-1/28-1/36-1/45-1/55-1/66-1/78-1/91-1/105-1/120=5/8
BẠN NÀO BIẾT THÌ GIÚP MÌNH VỚI !!!!!!!