#)Giải :

\(B=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{399}=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{19.21}\)

\(B=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}=\frac{1}{3}-\frac{1}{21}=\frac{2}{7}\)

\(C=\frac{7}{10.11}+\frac{7}{11.12}+\frac{7}{12.13}+...+\frac{7}{69.70}=7\left[\frac{1}{7}\left(\frac{7}{10.11}+\frac{7}{11.12}+...+\frac{7}{69.70}\right)\right]\)

\(C=7\left(\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+...+\frac{1}{69.70}\right)\)

\(C=7\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+...+\frac{1}{69}-\frac{1}{70}\right)\)

\(C=7\left(\frac{1}{10}-\frac{1}{70}\right)=7\times\frac{3}{35}=\frac{21}{35}\)

#)Góp ý :

Ý D tương tự ý C

giup toi voi toi dang can gap

a ) 15 / 90 x 94 + 15 / 94 x 98 + 15 / 98 x102+...+ 15 / 146 x 150

= 15/4 x ( 4/90 x 94 + 4/94 x 98 + ... + 4/ 146 x 150 )

= 15/4 x ( 1/90 - 1/94 + 1/94 - 1/98 + ... + 1/146 - 1/150 )

= 15/4 x ( 1/90 - 1/150 )

= 15/4 x 2/450

= 1/60

b ) 10 / 56 + 10/ 140 + 10 / 260+...+ 10 /1400

= 5/28 + 5/70 + 5/130 + ... + 5/700

= 5/4 x 7 + 5/7 x 10 + 5/10 x 13 + ... + 5 /25 x 28

= 5/3 x ( 3/4 x 7 + 3/7 x 10 + ... + 3/25 x 28 )

= 5/3 x ( 1/4 - 1/7 + 1/7 - 1/10 + ... + 1/25 - 1/28 )

= 5/3 x ( 1/4 - 1/28 )

= 5/3 x 6/28

= 5/14

a ) 15 / 90 x 94 + 15 / 94 x 98 + 15 / 98 x102+...+ 15 / 146 x 150

= 15/4 x ( 4/90 x 94 + 4/94 x 98 + ... + 4/ 146 x 150 )

= 15/4 x ( 1/90 - 1/94 + 1/94 - 1/98 + ... + 1/146 - 1/150 )

= 15/4 x ( 1/90 - 1/150 )

= 15/4 x 2/450

= 1/60

b ) 10 / 56 + 10/ 140 + 10 / 260+...+ 10 /1400

= 5/28 + 5/70 + 5/130 + ... + 5/700

= 5/4 x 7 + 5/7 x 10 + 5/10 x 13 + ... + 5 /25 x 28

= 5/3 x ( 3/4 x 7 + 3/7 x 10 + ... + 3/25 x 28 )

= 5/3 x ( 1/4 - 1/7 + 1/7 - 1/10 + ... + 1/25 - 1/28 )

= 5/3 x ( 1/4 - 1/28 )

= 5/3 x 6/28

= 5/14

Trịnh Thành Công có copy ở đâu ko mà sao làm(gõ) nhanh quá vậy?

a. \(\frac{15}{90.94}+\frac{15}{94.98}+\frac{15}{98.102}+...+\frac{15}{146.150}\)

\(=\frac{15}{4}.\left(\frac{1}{90}-\frac{1}{94}+\frac{1}{94}-\frac{1}{98}+...+\frac{1}{146}-\frac{1}{150}\right)\)

\(=\frac{15}{4}.\left(\frac{1}{90}-\frac{1}{150}\right)\)

\(=\frac{15}{4}.\frac{1}{225}\) \(=\frac{1}{60}\)

a ) 15 / 90 x 94 + 15 / 94 x 98 + 15 / 98 x102+...+ 15 / 146 x 150

= 15/4 x ( 4/90 x 94 + 4/94 x 98 + ... + 4/ 146 x 150 )

= 15/4 x ( 1/90 - 1/94 + 1/94 - 1/98 + ... + 1/146 - 1/150 )

= 15/4 x ( 1/90 - 1/150 )

= 15/4 x 2/450

= 1/60

b ) 10 / 56 + 10/ 140 + 10 / 260+...+ 10 /1400

= 5/28 + 5/70 + 5/130 + ... + 5/700

= 5/4 x 7 + 5/7 x 10 + 5/10 x 13 + ... + 5 /25 x 28

= 5/3 x ( 3/4 x 7 + 3/7 x 10 + ... + 3/25 x 28 )

= 5/3 x ( 1/4 - 1/7 + 1/7 - 1/10 + ... + 1/25 - 1/28 )

= 5/3 x ( 1/4 - 1/28 )

= 5/3 x 6/28

= 5/14

Tốn công quá !

a ) 15 / 90 x 94 + 15 / 94 x 98 + 15 / 98 x102+...+ 15 / 146 x 150

= 15/4 x ( 4/90 x 94 + 4/94 x 98 + ... + 4/ 146 x 150 )

= 15/4 x ( 1/90 - 1/94 + 1/94 - 1/98 + ... + 1/146 - 1/150 )

= 15/4 x ( 1/90 - 1/150 )

= 15/4 x 2/450

= 1/60

b ) 10 / 56 + 10/ 140 + 10 / 260+...+ 10 /1400

= 5/28 + 5/70 + 5/130 + ... + 5/700

= 5/4 x 7 + 5/7 x 10 + 5/10 x 13 + ... + 5 /25 x 28

= 5/3 x ( 3/4 x 7 + 3/7 x 10 + ... + 3/25 x 28 )

= 5/3 x ( 1/4 - 1/7 + 1/7 - 1/10 + ... + 1/25 - 1/28 )

= 5/3 x ( 1/4 - 1/28 )

= 5/3 x 6/28

= 5/14

thanks

\(A=\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}+...+\dfrac{1}{120}\)

\(A=\dfrac{2}{20}+\dfrac{2}{30}+\dfrac{2}{42}+...+\dfrac{2}{240}\)

\(A=\dfrac{2}{4.5}+\dfrac{2}{5.6}+\dfrac{2}{6.7}+...+\dfrac{2}{15.16}\)

\(A=2\left(\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+...+\dfrac{1}{15.16}\right)\)

\(A=2\left(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+...+\dfrac{1}{15}-\dfrac{1}{16}\right)\)

\(A=2\left(\dfrac{1}{4}-\dfrac{1}{16}\right)\)

\(A=2.\dfrac{3}{16}\)

\(A=\dfrac{3}{8}\)

\(B=\dfrac{4}{3.7}+\dfrac{4}{7.11}+\dfrac{4}{11.15}+...+\dfrac{4}{107.111}\)

\(B=\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{15}+...+\dfrac{1}{107}-\dfrac{1}{111}\)

\(B=\dfrac{1}{3}-\dfrac{1}{111}\)

\(B=\dfrac{12}{37}\)

\(C=\dfrac{7}{10.11}+\dfrac{7}{11.12}+\dfrac{7}{12.13}+...+\dfrac{7}{69.70}\)

\(C=7\left(\dfrac{1}{10.11}+\dfrac{1}{11.12}+\dfrac{1}{12.13}+...+\dfrac{7}{69.70}\right)\)

\(C=7\left(\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{13}+...+\dfrac{1}{69}-\dfrac{1}{70}\right)\)

\(C=7\left(\dfrac{1}{10}-\dfrac{1}{70}\right)\)

\(C=7.\dfrac{3}{35}\)

\(C=\dfrac{3}{5}\)

\(F=\frac{15}{90.94}+\frac{15}{94.98}+\frac{15}{98.102}+....+\frac{15}{146.150}\)

\(\Rightarrow F=\frac{15}{4}\left(\frac{15}{90}-\frac{15}{94}+\frac{15}{94}-\frac{15}{98}+....+\frac{15}{146}-\frac{15}{150}\right)\)

\(\Rightarrow F=\frac{15}{4}\left(\frac{1}{6}-\frac{1}{10}\right)=\frac{15}{4}\left(\frac{5}{30}-\frac{3}{30}\right)=\frac{15}{4}.\frac{1}{15}=\frac{15}{60}=\frac{1}{4}\)

Tk mình đi mọi người mình bị âm nè!

ai tk mình mình tk lại cho!!!

trả lời câu hỏi của mình đã

bạn Hà Chí Dương phải  giúp đỡ các bạn trả lời trên Online Math đừng có dụ dỗ các bạn tk mk như vậy

a) F = \(\frac{1}{25.27}+\frac{1}{27.29}+\frac{1}{29.31}+...+\frac{1}{73.75}\)

F = \(\frac{1}{2}.\left(\frac{1}{25}-\frac{1}{27}\right)+\frac{1}{2}.\left(\frac{1}{27}-\frac{1}{29}\right)+\frac{1}{2}.\left(\frac{1}{29}-\frac{1}{31}\right)+...+\frac{1}{2}.\left(\frac{1}{73}-\frac{1}{75}\right)\)

F = \(\frac{1}{2}.\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+\frac{1}{29}-\frac{1}{31}+...+\frac{1}{73}-\frac{1}{75}\right)\)

F = \(\frac{1}{2}.\left(\frac{1}{25}-\frac{1}{75}\right)\)

F = \(\frac{1}{2}.\frac{2}{75}\)

F = \(\frac{1}{75}\)

b) G = \(\frac{15}{90.94}+\frac{15}{94.98}+\frac{15}{98.102}+...+\frac{15}{146.150}\)

G = \(\frac{15}{4}.\frac{4}{90.94}+\frac{15}{4}.\frac{4}{94.98}+\frac{15}{4}.\frac{4}{98.102}+...+\frac{15}{4}.\frac{4}{146.150}\)

G = \(\frac{15}{4}.\left(\frac{1}{90}-\frac{1}{94}\right)+\frac{15}{4}.\left(\frac{1}{94}-\frac{1}{98}\right)+\frac{15}{4}.\left(\frac{1}{98}-\frac{1}{102}\right)+...+\frac{15}{4}.\left(\frac{1}{146}-\frac{1}{150}\right)\)

G = \(\frac{15}{4}.\left(\frac{1}{90}-\frac{1}{94}+\frac{1}{94}-\frac{1}{98}+\frac{1}{98}-\frac{1}{102}+...+\frac{1}{146}-\frac{1}{150}\right)\)

G = \(\frac{15}{4}.\left(\frac{1}{90}-\frac{1}{150}\right)\)

G = \(\frac{15}{4}.\frac{1}{225}\)

G = \(\frac{1}{60}\)

<br class="Apple-interchange-newline"><div id="inner-editor"></div>12.4 +14.6 +...+198.100 

=12 (22.4 +24.6 +...+298.100 )

<br class="Apple-interchange-newline"><div id="inner-editor"></div>=12 (12 −14 +14 −16 +...+198 −1100 )

<br class="Apple-interchange-newline"><div id="inner-editor"></div>=12 (12 −14 +14 −16 +...+198 −1100 )

<br class="Apple-interchange-newline"><div id="inner-editor"></div>=12 (12 −1100 )=12 .49100 =49200 

1056 +10140 +10260 +...+101400 =53 (

c) H = \(\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)

H = \(\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)

H = \(\frac{5}{3}.\frac{3}{28}+\frac{5}{3}.\frac{3}{70}+\frac{5}{3}.\frac{3}{130}+...+\frac{5}{3}.\frac{3}{700}\)

H = \(\frac{5}{3}.\left(\frac{3}{28}+\frac{3}{70}+\frac{3}{130}+...+\frac{3}{700}\right)\)

H = \(\frac{5}{3}.\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{25.28}\right)\)

H = \(\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)

H = \(\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{28}\right)\)

H = \(\frac{5}{3}.\frac{3}{14}\)

H = \(\frac{5}{14}\)