Tính: 24/29+7/38+31/38+15/24=...
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Lời giải:
$\frac{24}{19}+\frac{7}{38}+\frac{31}{38}+\frac{5}{38}$
$=\frac{48}{38}+\frac{7}{38}+\frac{31}{38}+\frac{5}{38}$
$=\frac{48+7+31+5}{38}=\frac{91}{38}$
\(\frac{24}{29}+\frac{7}{38}+\frac{31}{38}+\frac{5}{29}=\left(\frac{24}{29}+\frac{5}{29}\right)+\left(\frac{7}{38}+\frac{31}{38}\right)=\frac{29}{29}+\frac{38}{38}=1+1=2\)
=\(\dfrac{1}{18}-\dfrac{1}{23}+\dfrac{1}{23}-\dfrac{1}{24}+\dfrac{1}{24}-\dfrac{1}{31}+\dfrac{1}{31}-\dfrac{1}{33}+\dfrac{1}{33}-\dfrac{1}{37}+\dfrac{1}{37}-\dfrac{1}{38}\)
=\(\dfrac{1}{18}-\dfrac{1}{38}=\dfrac{19-9}{38x9}=\dfrac{10}{342}=\dfrac{5}{171}\)
\(\dfrac{5}{18\times23}+\dfrac{1}{23\times24}+\dfrac{7}{24\times31}+\dfrac{2}{31\times33}+\dfrac{4}{33\times37}+\dfrac{1}{37\tímes38}\)
\(\dfrac{23-18}{18\times23}+\dfrac{24-23}{23\times24}+\dfrac{31-24}{24\times31}+\dfrac{33-31}{31\times33}+\dfrac{37-33}{33\times37}+\dfrac{38-37}{37\times38}\)
\(\dfrac{23}{18\times23}-\dfrac{18}{18\times23}+\dfrac{24}{23\times24}-\dfrac{23}{23\times24}+\dfrac{31}{24\times31}-\dfrac{24}{24\times31}+\dfrac{33}{31\times33}-\dfrac{31}{31\times33}+\dfrac{37}{33\times37}-\dfrac{33}{33\times37}+\dfrac{38}{37\times38}-\dfrac{37}{37\times38}\)
\(\dfrac{1}{18}-\dfrac{1}{23}+\dfrac{1}{23}-\dfrac{1}{24}+\dfrac{1}{24}-\dfrac{1}{31}+\dfrac{1}{31}-\dfrac{1}{33}+\dfrac{1}{33}-\dfrac{1}{37}+\dfrac{1}{37}-\dfrac{1}{38}\)
\(\dfrac{1}{18}-\dfrac{38}=\dfrac{5}{171}\)
1/
$M=\frac{1}{3.8}+\frac{1}{8.13}+\frac{1}{13.18}+....+\frac{1}{33.38}$
$5M=\frac{8-3}{3.8}+\frac{13-8}{8.13}+\frac{18-13}{13.18}+...+\frac{38-33}{33.38}$
$=\frac{1}{3}-\frac{1}{8}+\frac{1}{8}-\frac{1}{13}+\frac{1}{13}-\frac{1}{18}+....+\frac{1}{33}-\frac{1}{38}$
$=\frac{1}{3}-\frac{1}{38}=\frac{35}{114}$
$\Rightarrow M=\frac{35}{114}:5=\frac{7}{114}$
2/
$N=\frac{1}{3.10}+\frac{1}{10.17}+\frac{1}{17.24}+\frac{1}{24.31}+\frac{1}{31.38}$
$7N=\frac{10-3}{3.10}+\frac{17-10}{10.17}+\frac{24-17}{17.24}+\frac{31-24}{24.31}+\frac{38-31}{31.38}$
$=\frac{1}{3}-\frac{1}{10}+\frac{1}{10}-\frac{1}{17}+\frac{1}{17}-\frac{1}{24}+\frac{1}{24}-\frac{1}{31}+\frac{1}{31}-\frac{1}{38}$
$=\frac{1}{3}-\frac{1}{38}=\frac{35}{114}$
$\Rightarrow N=\frac{35}{114}:7=\frac{5}{114}$
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