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#)Giải :
\(S=\frac{38}{25}+\frac{9}{10}-\frac{11}{15}+\frac{13}{21}-\frac{15}{28}+\frac{17}{36}-\frac{19}{45}+...-\frac{119}{4950}\)
\(S=\frac{38}{25}+\left(\frac{9}{10}-\frac{11}{15}\right)+\left(\frac{13}{21}-\frac{15}{28}\right) +\left(\frac{17}{36}-\frac{19}{45}\right)+...+\left(\frac{197}{4851}-\frac{199}{4950}\right)\)
Ta thấy :
\(\left(\frac{9}{10}-\frac{11}{15}\right)=\frac{1}{6}=\frac{1}{\left(2.3\right)}=\frac{1}{2}-\frac{1}{3}\)
\(\left(\frac{13}{21}-\frac{15}{28}\right)=\frac{1}{12}=\frac{1}{\left(3.4\right)}=\frac{1}{3}-\frac{1}{4}\)
\(\left(\frac{17}{36}-\frac{19}{45}\right)=\frac{1}{20}=\frac{1}{\left(4.5\right)}=\frac{1}{4}-\frac{1}{5}\)
..........................................................
\(\left(\frac{197}{4851}-\frac{199}{4950}\right)=\frac{1}{2450}=\frac{1}{\left(49.50\right)}=\frac{1}{49}-\frac{1}{50}\)
\(\Rightarrow S=\frac{38}{25}+\left[\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{5}\right)+...+\left(\frac{1}{49}-\frac{1}{50}\right)\right]\)
\(\Rightarrow S=\frac{38}{25}+\left[\frac{1}{2}-\frac{1}{50}\right]\)
\(\Rightarrow S=\frac{38}{25}+\frac{24}{50}\)
\(\Rightarrow S=2\)
#~Will~be~Pens~#
bỏ tạm 38/25 ra
=(9/10-11/15) +(13/21-15/28) +(197/4851-199/4950)
=1/6+1/12+1/20+...+1/49*50=2450
=3-2/2x3+4-3/3x4+5-4/4x5+....50-49/49x50
=1/2-1/3+1/3-...-1/50
1/2-1/50=12/25
=38/25+12/25=50/25
=2
( x + 1 ) + ( x + 4 ) + ( x + 7 ) + ......... + ( x + 28 ) = 155
<=>(x+x+x...+x)+(1+4+...+28)=155
=>10x+145=155
=>10x=155-145
=>10x=10
=>x=1
\(\dfrac{7}{19}x\dfrac{8}{23}+\dfrac{7}{19}x\dfrac{15}{23}+1\dfrac{7}{19}\)
= \(\dfrac{7}{19}x\left(\dfrac{8}{23}+\dfrac{15}{23}\right)+1+\dfrac{7}{19}\)
=\(\dfrac{7}{19}x1+1+\dfrac{7}{19}\)
= \(\dfrac{7}{19}+1+\dfrac{7}{19}=1\dfrac{14}{19}\) = \(\dfrac{33}{19}\)
\(\dfrac{75}{100}+\dfrac{18}{21}+\dfrac{49}{32}+\dfrac{1}{4}+\dfrac{3}{21}-\dfrac{17}{32}\)
= \(\dfrac{3}{4}+\dfrac{6}{7}+\dfrac{49}{32}+\dfrac{1}{4}+\dfrac{1}{7}-\dfrac{17}{32}\)
= \(\left(\dfrac{3}{4}+\dfrac{1}{4}\right)+\left(\dfrac{6}{7}+\dfrac{1}{7}\right)+\left(\dfrac{49}{32}-\dfrac{17}{32}\right)\)
= 1 + 1 + 1 = 3
\(\dfrac{8}{9}x\dfrac{15}{16}x\dfrac{24}{25}x\dfrac{35}{36}x\dfrac{48}{49}x\dfrac{63}{64}\)
= \(\dfrac{3}{4}\) *Câu này bạn tự sử dụng gạch nhé!
`1,`
`a,`
`7/19 \times 8/23 + 7/19 \times 15/23 + 1 7/19`
`= 7/19 \times 8/23 + 7/19 \times 15/23 + 1 + 7/19`
`= 7/19 \times (8/23 + 15/23 + 1) + 1`
`= 7/19 \times 2 + 1`
`=14/19 + 1`
`= 33/19`
`b,`
`75/100 + 18/21 + 49/32 + 1/4 + 3/21 - 17/32`
`= 75/100 + (18/21 + 3/21) + (49/32 - 17/32) + 1/4`
`= 0,75 + 1 + 1 + 0,25`
`= (0,75 + 0,25) + 1 + 1`
`= 1+1+1=3`
`c,`
`8/9 \times 15/16 \times 24/25 \times 35/36 \times 48/49 \times 63/64`
`=` \(\dfrac{2\times3}{3\times3}\times\dfrac{3\times5}{4\times4}\times\dfrac{3\times4\times2}{5\times5}\times\dfrac{5\times7}{6\times6}\times\dfrac{6\times8}{7\times7}\times\dfrac{7\times9}{8\times8}\)
`= 3/4` (bạn sử dụng gạch, rút gọn các số là được nhé).
9/120 nha bạn