A=120+130+142+156+172+190+1110 B=16+215+340+5104+8273+13714

A=120+130+142+156+172+190+1110 ...

pls help me

· 21:04 08/09/2021

A= $\frac{1}{20} + \frac{1}{30} + \frac{1}{42} + \frac{1}{56} + \frac{1}{72} + \frac{1}{90} + \frac{1}{110}$
B= $\frac{1}{6} + \frac{2}{15} + \frac{3}{40} + \frac{5}{104} + \frac{8}{273} + \frac{13}{714}$

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5 năm trước

\[\begin{array}{l}
A = \frac{1}{{20}} + \frac{1}{{30}} + \frac{1}{{42}} + \frac{1}{{56}} + \frac{1}{{72}} + \frac{1}{{90}} + \frac{1}{{110}}\\
= \frac{1}{{4.5}} + \frac{1}{{5.6}} + \frac{1}{{6.7}} + \frac{1}{{7.8}} + \frac{1}{{8.9}} + \frac{1}{{9.10}} + \frac{1}{{10.11}}\\
= \frac{1}{4} - \frac{1}{5} + \frac{1}{5} - \frac{1}{6} + \frac{1}{6} - \frac{1}{7} + \frac{1}{7} - \frac{1}{8} + \frac{1}{8} - \frac{1}{9} + \frac{1}{9} - \frac{1}{{10}} + \frac{1}{{10}} - \frac{1}{{11}}\\
= \frac{1}{4} - \frac{1}{{11}}\\
= \frac{{11 - 4}}{{44}}\\
= \frac{7}{{44}}\\
vay:A = \frac{7}{{44}}
\end{array}\]

\[\begin{array}{l}
B = \frac{1}{6} + \frac{2}{{15}} + \frac{3}{{40}} + \frac{5}{{104}} + \frac{8}{{273}} + \frac{{13}}{{714}}\\
= \frac{1}{{2.3}} + \frac{2}{{3.5}} + \frac{3}{{5.8}} + \frac{5}{{8.13}} + \frac{8}{{13.21}} + \frac{{13}}{{21.34}}\\
= \frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{5} + \frac{1}{5} - \frac{1}{8} + \frac{1}{8} - \frac{1}{{13}} + \frac{1}{{13}} - \frac{1}{{21}} + \frac{1}{{21}} - \frac{1}{{34}}\\
= \frac{1}{2} - \frac{1}{{34}}\\
= \frac{{17 - 1}}{{34}}\\
= \frac{{16}}{{34}}\\
= \frac{8}{{17}}\\
vay:B = \frac{8}{{17}}
\end{array}\]

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Maianh

5 năm trước