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a) Đặt A= \(\dfrac{1}{3}+\dfrac{1}{6}+...+\dfrac{1}{36}\)
\(\dfrac{1}{2}\)A=\(\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{72}\)
\(\dfrac{1}{2}\)A=\(\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{8.9}\)
\(\dfrac{1}{2}\)A=\(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{8}-\dfrac{1}{9}\)
\(\dfrac{1}{2}\)A=\(\dfrac{1}{2}-\dfrac{1}{9}\)
\(\dfrac{1}{2}\)A=\(\dfrac{7}{18}\)
A=\(\dfrac{7}{9}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
trả lời nhanh giúp mink nhé mink đang rất cần nếu ai trả lời đúng mink sẽ tặng điểm
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a, \(\frac{3}{5}+\frac{-4}{15}=\frac{9}{15}-\frac{4}{15}=\frac{5}{15}=\frac{1}{3}\)
b, \(\frac{-1}{3}+\frac{2}{5}+\frac{2}{15}=\frac{-5}{15}+\frac{6}{15}+\frac{2}{15}=\frac{3}{15}=\frac{1}{5}\)
c, \(\frac{-3}{5}+\frac{7}{21}+\frac{-4}{5}+\frac{7}{5}=\frac{-3}{5}+\frac{1}{3}+\frac{-4}{5}+\frac{7}{5}=\left(\frac{-3}{5}+\frac{-4}{5}+\frac{7}{5}\right)+\frac{1}{3}=\frac{1}{3}\)
d, \(\frac{2}{7}+\frac{1}{9}+\frac{3}{7}+\frac{5}{9}+\frac{-5}{6}=\left(\frac{2}{7}+\frac{3}{7}\right)+\left(\frac{1}{9}+\frac{5}{9}\right)+\frac{-5}{6}=\frac{5}{7}+\frac{6}{9}+\frac{-5}{6}=\frac{90}{126}+\frac{84}{126}+\frac{-105}{126}=\frac{69}{126}=\frac{23}{42}\)
e, \(\frac{-5}{7}+\frac{3}{4}+\frac{-1}{5}+\frac{-2}{7}+\frac{1}{4}=\left(\frac{-5}{7}+\frac{-2}{7}\right)+\left(\frac{3}{4}+\frac{1}{4}\right)+\frac{-1}{5}=\left(-1\right)+1+\frac{-1}{5}=\frac{-1}{5}\)
f, \(\frac{-3}{31}+\frac{-6}{17}+\frac{1}{25}+\frac{-28}{31}+\frac{-1}{17}+\frac{-1}{5}=\left(\frac{-3}{31}+\frac{-28}{31}\right)+\left(\frac{-6}{17}+\frac{-1}{17}\right)+\left(\frac{1}{25}+\frac{-1}{5}\right)=\left(-1\right)+\frac{-7}{17}+\frac{-4}{25}=\frac{-425}{425}+\frac{-175}{425}+\frac{-68}{425}=\frac{-668}{425}\)
Chúc bn học tốt
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ta thấy \(\frac{1}{20}\)<\(\frac{1}{3}\)
thì \(\frac{1}{20}\)+...+\(\frac{1}{29}\)<\(\frac{1}{20}\)+...+\(\frac{1}{20}\)<\(\frac{1}{3}\)
vậy \(\frac{1}{20}\)+...+\(\frac{1}{29}\)<\(\frac{1}{3}\)
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Chứng minh :
\(S=\frac{1}{5}+\frac{1}{21}+\frac{1}{22}+...+\frac{1}{25}+\frac{1}{101}+\frac{1}{102}+...+\frac{1}{105}< \frac{1}{2}\)
Nhóm các số hạng:
\(S=\frac{1}{5}+\left(\frac{1}{21}+\frac{1}{22}+...+\frac{1}{25}\right)+\left(\frac{1}{101}+\frac{1}{102}+...+\frac{1}{105}\right)< \frac{1}{5}+\frac{5}{21}+\frac{5}{101}< \frac{1}{5}+\frac{5}{20}+\frac{5}{100}=\frac{1}{2}.\)
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13/30+(-1)/5=13/30+(-6)/30=7/30
2/21+1/28=8/84+3/84=11/84
*Dấu phân số đc thay bởi dấu /
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đề có vấn đề