1320 ta

3x/2.5 + 3x/5.8 + 3x/8.11 + 3x/11.14 = 1/21

=> x . ( 3/2.5 + 3/5.8 + 3/8.11 + 3/11.14 ) = 1/21

=> x . ( 1/2.5 + 1/5.8 + 1/8.11 + 1/11.14 ) = 1/21

x . ( 1/2 - 1/5 + 1/5 - 1/8 + 1/8 - 1/11 + 1/11 - 1/14 ) = 1/21

x . ( 1/2 - 1/14 ) = 1/21

x . 3/7 = 1/21 

x = 1/21 : 3/7

=> x = 1/9

\(\frac{3x}{2\cdot5}+\frac{3x}{5\cdot8}+\frac{3x}{8\cdot11}+\frac{3x}{11\cdot14}=\frac{1}{21}\)

<=> \(x\left(\frac{3}{2\cdot5}+\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+\frac{3}{11\cdot14}\right)=\frac{1}{21}\)

<=> \(x\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}\right)=\frac{1}{21}\)

<=> \(x\left(\frac{1}{2}-\frac{1}{14}\right)=\frac{1}{21}\)

<=> \(x\cdot\frac{3}{7}=\frac{1}{21}\)

<=> \(x=\frac{1}{9}\)

3/2.5 + ...+ 3/17 .20

= 3/2 .(1/2 - 1/5 + 1/5 - 1/8 + ... + 1/17 - 120)

= 3/2 . (1/2 - 1/20)

= \(\frac{3}{2}\) . \(\frac{9}{20}\) = \(\frac{27}{40}\)

P= 3/ 2.5 + 3/5.8 + 3/8.11 + .... + 3/17.20

P= 1/2 - 1/5 + 1/5 - 1/8 + 1/8 - 1/11 + .... + 1 /17 - 1/20

P= 1 / 2 - 1 / 20

P = 9/20

\(P=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{17.20}\)

\(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{17}-\frac{1}{20}\)

\(=\frac{1}{2}-\frac{1}{20}\)

\(\frac{9}{20}\)

\(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{62.65}\)

\(=1.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{62}-\frac{1}{65}\right)\)

\(=1.\left(\frac{1}{2}-\frac{1}{65}\right)\)

\(=1.\frac{63}{130}\)

\(=\frac{63}{130}\)

Bài làm

       \(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{62.65}\)

\(=3.\frac{1}{2.5}+3.\frac{1}{5.8}+3.\frac{1}{8.11}+...+3.\frac{1}{62.65}\)

\(=3.\left(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{62.65}\right)\)

\(=3.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{62}-\frac{1}{65}\right)\)

\(=3.\left(\frac{1}{2}-\frac{1}{65}\right)\)

\(=3.\left(\frac{65}{130}-\frac{2}{130}\right)\)

\(=3.\frac{63}{130}\)

\(=\frac{3.63}{130}\)

\(=\frac{189}{130}\)

# Chúc bạn học tốt #

1/2.5+1/5.8+1/8.11+...+1/29.32 (khoảng cách từ 2-5;5-8;8-11;...;29-32 là 3) suy ra

=1/3(1/2-1/5+1/5-1/8+1/8-1/11+...+1/29-1/32)  (-1/5+1/5;-1/8+1/8;-1/11+1/11=0) suy ra =1/3(1/2-1/32)=1/3.15/32=5/32

1/2.5+1/5.8+1/8.9+............+1/29.32

=1/2-1/5+1/5-1/8+...............+1/29-1/32

=1/2-1/32

=15/32

ai tích mk=>mk tích lại

\(\frac{12}{2.5}+\frac{12}{5.8}+\frac{12}{8.11}+...+\frac{12}{29.32}\)

\(=4.\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{29.32}\right)\)

\(=4.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{29}-\frac{1}{32}\right)\)

\(=4.\left(\frac{1}{2}-\frac{1}{32}\right)\)

\(=4.\frac{15}{32}\)

\(=\frac{15}{8}\)

_Chúc bạn học tốt_

\(\frac{12}{2.5}+\frac{12}{5.8}+\frac{12}{8.11}+....+\frac{12}{29.32}\)

\(=4\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{29.32}\right)\)

\(=4\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{29}-\frac{1}{32}\right)\)

\(=4\left(\frac{1}{2}-\frac{1}{32}\right)\)

\(=4.\frac{15}{32}=\frac{15}{8}\)

Đặt A= 12/2*5+12/5*8+12/8*11+....+12/29*32

       A= 4*(3/2*5+3/5*8+3/8*11+...+3/29*32)

       A = 4*(1/2-1/5+1/5-1/8+1/8-1/11+....+1/29-1/32)

       A= 4*(1/2-1/32)

       A= 4*15/32

       A= 15/8

\(S=2.\left(\frac{3}{2.5}+\frac{3}{5.8}+...+\frac{3}{29.32}\right)\)

\(S=2.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{29}-\frac{1}{32}\right)\)

\(S=2.\left(\frac{1}{2}-\frac{1}{32}\right)\)

\(S=1-\frac{1}{16}< 1\)

Vậy \(S< 1\)