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A= 3/11*16+3/16*21+3/21*26+.....+3/61*66
\(=\frac{3}{5}\left(\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{61.66}\right)\)
\(=\frac{3}{5}\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\right)\)
\(=\frac{3}{5}\left(\frac{1}{11}-\frac{1}{66}\right)\)
\(=\frac{3}{5}\cdot\frac{5}{66}\)
\(=\frac{1}{22}\)
\(A=\frac{3}{11.16}+\frac{3}{16.21}+\frac{3}{21.26}+...+\frac{3}{61.66}\)
\(\Rightarrow A=\frac{3}{5}\left(\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+...+\frac{5}{61.66}\right)\)
\(\Rightarrow A=\frac{3}{5}.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\right)\)
\(\Rightarrow A=\frac{3}{5}.\left(\frac{1}{11}-\frac{1}{66}\right)\)
\(\Rightarrow A=\frac{3}{5}.\frac{5}{66}\)
\(\Rightarrow A=\frac{1}{22}\)
Vậy \(A=\frac{1}{22}\)
Tổng trên bằng:
[1 + (-6)] + [11 + (-16)] + [21 + (-26)] + [31 + (-36)]
= (-5) + (-5) +(-5) + (-5)
= (-5) x 4
= -20
\(=1-6+11-16+21-26+31-36.\)
\(=\left(1+11+21+31\right)-\left(6+16+26+36\right)\)
Đây là Hiệu của hai dãy số cách đều có khỏng cách là 10. Tự làm nốt nhé
\(=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\)
\(=\frac{1}{11}-\frac{1}{66}=\frac{6}{66}-\frac{1}{66}=\frac{5}{66}\)
1: Ta có: \(2155-\left(174+2155\right)+\left(-68+174\right)\)
\(=2155-174-2155-68+174\)
=-68
2) Ta có: \(-25\cdot72+25\cdot21-49\cdot25\)
\(=-25\cdot\left(72-21+49\right)\)
\(=-25\cdot100=-2500\)
a) \(...=-\dfrac{12}{46}-\dfrac{15}{21}+\dfrac{3}{7}-\dfrac{7}{23}\)
\(=-\dfrac{12}{46}-\dfrac{7}{23}-\dfrac{15}{21}+\dfrac{3}{7}\)
\(=-\dfrac{6}{23}-\dfrac{7}{23}-\dfrac{5}{7}+\dfrac{3}{7}\)
\(=-\dfrac{13}{23}-\dfrac{2}{7}\)
\(=-\dfrac{13.7}{23.7}-\dfrac{2.23}{23.7}\)
\(=-\dfrac{91}{161}-\dfrac{46}{161}=-\dfrac{137}{161}\)
b) \(...=-21+\dfrac{7}{9}-\dfrac{3}{17}+\dfrac{25}{9}\)
\(=-21-\dfrac{3}{17}+\dfrac{7}{9}+\dfrac{25}{9}\)
\(=-21-\dfrac{3}{17}+\dfrac{32}{9}\)
\(=-\dfrac{3213}{153}-\dfrac{27}{153}+\dfrac{544}{153}=-\dfrac{2696}{153}\)
a, \(\frac{4}{20}+\frac{16}{42}+\frac{6}{15}+\frac{-3}{5}+\frac{-10}{21}+\frac{3}{20}\)
\(=\left(\frac{4}{20}+\frac{-3}{5}+\frac{6}{15}+\frac{3}{20}\right)\)\(+\left(\frac{16}{42}+\frac{2}{21}+\frac{-10}{21}\right)\)
\(=\left(\frac{4}{20}+\frac{-12}{20}+\frac{8}{20}+\frac{3}{20}\right)\)\(+\left(\frac{8}{21}+\frac{2}{21}+\frac{-10}{21}\right)\)
\(=\frac{3}{20}\)
b,\(\frac{42}{46}+\frac{250}{186}+\frac{-2121}{2323}+\frac{-125125}{143143}\)
\(=\frac{21}{23}+\frac{125}{93}+\frac{-21}{23}+\frac{-125}{143}\)
\(=\left(\frac{21}{23}+\frac{-21}{23}\right)+\left(\frac{125}{93}+\frac{-125}{143}\right)\)
\(=\frac{6250}{13299}\)
\(\dfrac{55}{11}\cdot6+\dfrac{55}{16}\cdot21+\dfrac{55}{21}\cdot26+\dfrac{55}{26}\cdot31+\dfrac{55}{31}\cdot36+\dfrac{55}{36}\cdot41=30+\dfrac{1155}{16}+\dfrac{1430}{21}+\dfrac{1705}{26}+\dfrac{1980}{31}+\dfrac{2255}{36}=\dfrac{12186720}{406224}+\dfrac{29324295}{406224}+\dfrac{27661920}{406224}+\dfrac{26638920}{406224}+\dfrac{25945920}{406224}+\dfrac{25445420}{406224}=\dfrac{147203195}{406224}\)
\(21+21+21+...+21+21+16+16+16+...+16.\) (84 số 21 và 21 số 16)
\(=84\cdot21+21\cdot16=21\left(84+16\right)=21\cdot100=2100\)
21.84+21.16=21(84+16)=21.100=2100