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\(C=\dfrac{7}{10.11}+\dfrac{7}{11.12}+\dfrac{7}{12.13}+...+\dfrac{7}{69.70}\)
= \(7\left(\dfrac{1}{10.11}+\dfrac{1}{11.12}+\dfrac{1}{12.13}+...+\dfrac{1}{69.70}\right)\)
= \(7\left(\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{13}+...+\dfrac{1}{69}-\dfrac{1}{70}\right)\)
= \(7\left(\dfrac{1}{10}-\dfrac{1}{70}\right)\)
=\(7\left(\dfrac{7}{70}-\dfrac{1}{70}\right)\)
= \(7.\dfrac{6}{70}\)
= \(\dfrac{3}{5}\)
\(a)\dfrac{3}{4}+\dfrac{6}{12}-\dfrac{5}{24}\)
\(=\dfrac{18}{24}+\dfrac{12}{24}+\left(-\dfrac{5}{24}\right)\)
\(=\dfrac{18+12+\left(-5\right)}{24}\)
\(=\dfrac{25}{24}\)
\(b)\dfrac{-5}{7}.\dfrac{2}{13}-\dfrac{5}{7}.\dfrac{11}{13}+\dfrac{5}{7}\)
\(=\dfrac{5}{7}.\dfrac{-2}{13}-\dfrac{5}{7}.\dfrac{11}{13}+\dfrac{5}{7}\)
\(=\dfrac{5}{7}\left(\dfrac{-2}{13}+\dfrac{-11}{13}+\dfrac{13}{13}\right)\)
\(=\dfrac{5}{7}.0=0\)
\(c)\dfrac{27}{23}+\dfrac{5}{21}+\dfrac{1}{2}-\dfrac{4}{23}+\dfrac{16}{21}\)
\(=\left(\dfrac{27}{23}-\dfrac{4}{23}\right)+\left(\dfrac{5}{21}+\dfrac{16}{21}\right)+\dfrac{1}{2}\)
\(=1+1+\dfrac{1}{2}\)
\(=2\dfrac{1}{2}\)
\(d)\dfrac{15}{34}+\dfrac{7}{21}+\dfrac{19}{34}.\dfrac{20}{15}+\dfrac{3}{7}\)
\(=\dfrac{315}{714}+\dfrac{238}{714}+\dfrac{38}{51}+\dfrac{306}{714}\)
\(=\dfrac{315}{714}+\dfrac{238}{714}+\dfrac{532}{714}+\dfrac{306}{714}\)
\(=\dfrac{1391}{714}\)
a)\(\dfrac{3}{4}+\dfrac{6}{12}-\dfrac{5}{24}=\dfrac{18}{24}+\dfrac{12}{24}-\dfrac{5}{24}=\dfrac{25}{24}\)
b)\(\dfrac{-5}{7}.\dfrac{2}{13}-\dfrac{5}{7}.\dfrac{11}{13}+\dfrac{5}{7}=\dfrac{5}{7}\left(\dfrac{-2}{13}-\dfrac{11}{13}+1\right)=\dfrac{5}{7}.0=0\)
c)\(\dfrac{27}{23}+\dfrac{5}{21}+\dfrac{1}{2}-\dfrac{4}{23}+\dfrac{16}{21}=\left(\dfrac{27}{23}-\dfrac{4}{23}\right)+\left(\dfrac{5}{21}+\dfrac{16}{21}\right)+\dfrac{1}{2}=1+1+\dfrac{1}{2}=2,5\)
d)\(\dfrac{15}{34}+\dfrac{7}{21}+\dfrac{19}{34}.\dfrac{20}{15}+\dfrac{3}{7}=\dfrac{15}{34}+\left(\dfrac{1}{3}+\dfrac{38}{51}+\dfrac{3}{7}\right)=\dfrac{15}{34}+\dfrac{538}{357}=\dfrac{1391}{714}\)
1,
\(S=-\dfrac{7}{20}-\dfrac{7}{200}-\dfrac{7}{2000}-\dfrac{7}{20000}\\ =-\dfrac{7}{20}\left(1+\dfrac{1}{10}+\dfrac{1}{100}+\dfrac{1}{1000}\right)\\ =-\dfrac{7}{20}\left(\dfrac{1000+100+10+1}{1000}\right)\\ =-\dfrac{7}{20}\cdot\dfrac{1111}{1000}\\ =\dfrac{7777}{20000}\)
2,
a, \(Tacó:\\ 9^{2000}=\left(3^2\right)^{2000}=3^{4000}\\ \Rightarrow9^{2000}=3^{4000}\)
b,
\(2^{225}=\left(2^{15}\right)^{15}=32768^{15}\\ 3^{150}=\left(3^{10}\right)^{15}=59049^{15}\\ Vì32768< 59049nên32768^{15}< 59049^{15}\\ \Rightarrow2^{225}< 3^{150}\)
3,
\(\left|x-7\right|=x-7\\ Vì\left|x-7\right|\ge0\forall x\\ \Rightarrow x-7\ge0\forall x\\ \Leftrightarrow x-7\ge0\\ \Leftrightarrow x\ge7\\ Vậyx\ge7\)
Bài 3:
\(\left|x-7\right|=x-7\)
Khi giá trị tuyệt đối của \(x-7\) bằng chính nó, thì \(x-7\) phải \(\ge0\)
Suy ra: \(x-7\ge0\Rightarrow x\ge7\)
Vậy \(x\ge 7\)
Số thập phân hữu hạn là mấy số thập phân không có dấu .... ở đuôi ý bạn ạ.
Còn bài này mình không hiểu rõ đề bài mấy bạn ạ
a/Ta có: \(\dfrac{4}{3}-\left[\left(\dfrac{-11}{6}\right)-\left(\dfrac{2}{9}+\dfrac{5}{3}\right)\right]\)
\(=\) \(\dfrac{4}{3}-\left[\dfrac{-11}{6}-\dfrac{2}{9}-\dfrac{5}{3}\right]\)
\(=\) \(\dfrac{4}{3}+\dfrac{11}{6}+\dfrac{2}{9}+\dfrac{5}{3}\)
\(=\) \(\dfrac{24}{18}+\dfrac{33}{18}+\dfrac{4}{18}+\dfrac{30}{18}\)
\(=\) \(\dfrac{91}{18}\)
b/Ta có: \(\left(8-\dfrac{9}{4}+\dfrac{2}{7}\right)-\left(-6-\dfrac{3}{7}+\dfrac{5}{4}\right)-\left(3+\dfrac{2}{4}-\dfrac{9}{7}\right)\)
\(=\) \(8-\dfrac{9}{4}+\dfrac{2}{7}+6+\dfrac{3}{7}-\dfrac{5}{4}-3-\dfrac{2}{4}+\dfrac{9}{7}\)
\(=\) \(8+6-3-\dfrac{9}{4}-\dfrac{5}{4}-\dfrac{2}{4}+\dfrac{2}{7}+\dfrac{3}{7}+\dfrac{9}{7}\)
\(=\) \(11-\dfrac{2}{4}+\dfrac{14}{7}\)
\(=\) \(11-\dfrac{1}{2}+2\)
\(=\) \(9-\dfrac{1}{2}\)
\(=\) \(\dfrac{17}{2}\)
Chúc bn học tốt!!!
A)0,25:(10,3-9,8)-3/4
=1/4:(103/10-49/5)-3/4
=1/4:1/2-3/4
=1/2-3/4
=2/4-3/4
=-1/4
B)-5/9.13/28-13/28.4/9
=-5/9-4/9.13/28
=-1.13/28
=-13/28
c)6/7+5/8:5-3/16
=6/7+1/8-3/16
=55/56-3/16
=89/112
d)-5/7.2/11+-5/7.9/11+1/5/7
=-5/7.(2/11+9/11)+12/7
=-5/7.1+12/7
=-5/7+12/7
=1
e)-7/12-8/15+11/20
=-67/60+11/20
=-17/30
f)-17/25.20/33+-17/25.13/33+-3/25
=-17/25.(20/33+13/33)-3/25
=-17/25.1-3/25
=-17/25-3/25
=-4/5
CHÚC BẠN HỌC TỐT...............
NẾU ĐÚNG THÌ TICK CHO MK VỚI NHA HELLO HELLO..........
\(\dfrac{7}{110}+\dfrac{7}{132}+\dfrac{7}{156}+...+\dfrac{7}{4830}\)
\(=\dfrac{7}{10\cdot11}+\dfrac{7}{11\cdot12}+\dfrac{7}{12\cdot13}+...+\dfrac{7}{69\cdot70}\)
\(=7\left(\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{13}+...+\dfrac{1}{69}-\dfrac{1}{70}\right)\)
\(=7\left(\dfrac{1}{10}-\dfrac{1}{70}\right)\)
\(=7\cdot\dfrac{3}{35}=\dfrac{3}{5}\)