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a) \(74\frac{19}{35}.\frac{7}{90}+15\frac{16}{35}.\frac{7}{90}+2\frac{14}{90}\)
= \(\left(74\frac{19}{35}+15\frac{16}{35}\right).\frac{7}{90}+2\frac{14}{90}\)
= 90 . 7/90 + 194/90
= 630/90 + 194/90
= 824/90 = 412/45
b) (-2/5 + 3/7) - (4/9 + 12/20 - 13/35) + 7/35
= -2/5 + 3/7 - 4/9 - 3/5 + 13/35 + 7/35
= (-2/5 - 3/5) + 3/7 - 4/9 + (13/35 + 7/35)
= -1 + 3/7 - 4/9 + 4/7
= -1 + (3/7 + 4/7) - 4/9
= -1 + 1 - 4/9 = -4/9
A=.....
=\(7.\left(\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+....+\frac{1}{69.70}\right)=7.\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+.....+\frac{1}{69}-\frac{1}{70}\right)\)
=\(7.\left(\frac{1}{10}-\frac{1}{70}\right)=7.\frac{3}{35}=\frac{3}{5}\)
MẤY PHẦN SAU CX TÁCH MẪU RA RÙI LÀM NHƯ VẬY
TỰ LÀM NHE
\(B=\frac{1}{3\cdot6}+\frac{1}{6\cdot9}+...+\frac{1}{30\cdot33}\)
\(B=\frac{1}{3}\cdot\left(\frac{3}{3\cdot6}+\frac{3}{6\cdot9}+...+\frac{3}{30\cdot33}\right)\)
\(B=\frac{1}{3}\cdot\left(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+...+\frac{1}{30}-\frac{1}{33}\right)\)
\(B=\frac{1}{3}\cdot\left(\frac{1}{3}-\frac{1}{33}\right)\)
\(B=\frac{1}{3}\cdot\frac{10}{33}=\frac{10}{99}\)
\(C=\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{6}\right)+...+\left(1-\frac{1}{90}\right)\)
\(C=\left(1-\frac{1}{1\cdot2}\right)+\left(1-\frac{1}{2\cdot3}\right)+...+\left(1-\frac{1}{9\cdot10}\right)\)
\(C=9-\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{9\cdot10}\right)\)
\(C=9-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(C=9-\left(1-\frac{1}{10}\right)\)
\(C=9-\frac{9}{10}=\frac{81}{10}\)
1/ Tính:
\(\frac{3}{2}-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}\)
\(=\frac{3}{1.2}-\frac{5}{2.3}+\frac{7}{3.4}-\frac{9}{4.5}+\frac{11}{5.6}-\frac{13}{6.7}+\frac{15}{7.8}-\frac{17}{8.9}+\frac{19}{9.10}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)
\(=1-\frac{1}{10}\)
\(=\frac{9}{10}\)
1/ \(\frac{9.5^{20}.27^9-3.9^{15}.25^9}{7.3^{29}.125^6-3.3^9.15^{19}}\)
\(=\frac{5^{20}.3^{29}-3^{31}.5^{18}}{7.3^{29}.5^{18}-3^{29}.5^{19}}=\frac{3^{29}.5^{18}.\left(25-9\right)}{3^{29}.5^{18}.\left(7-5\right)}=\frac{16}{2}=8\)
CÁC BÀI CÒN LẠI TƯƠNG TỰ HẾT NHÉ E
\(\frac{3}{2^2}\)+\(\frac{5}{6^2}\)+\(\frac{7}{12^2}\)+ ....+\(\frac{19}{90^2}\)
= \(\frac{3}{4}\)+\(\frac{5}{36}\)+\(\frac{7}{144}\)+....+\(\frac{19}{8100}\)
= (\(\frac{3}{4}\)+\(\frac{5}{36}\)+\(\frac{7}{144}\)) + .... \(\frac{19}{8100}\)
= (\(\frac{108}{144}\)+\(\frac{20}{144}\)+\(\frac{7}{144}\)) +....+\(\frac{19}{8100}\)
= \(\frac{108+20+7}{144}\)+....+\(\frac{19}{8100}\)
=\(\frac{135}{144}\)+....+\(\frac{19}{8100}\)
=\(\frac{7593,75}{8100}\)+....+\(\frac{19}{8100}\)
=\(\frac{7593,75}{8100}\)+\(\frac{19}{8100}\)
=\(\frac{7593,75+19}{8100}\)
=\(\frac{7612,75}{8100}\)
mik không chắc đúng không?
=3/4+5/36+......+19/8100
=3/1.4+5/4.9+.............+19/81.100
=1/1-1/4+1/4-1/9+...............+1/81-1/90
=1/1-1/90=1-1/90=89/90