Ta có:

\(A=\frac{1}{7}+\frac{1}{91}+\frac{1}{247}+\frac{1}{475}+\frac{1}{775}+\frac{1}{1147}\)

\(=\frac{1}{1.7}+\frac{1}{7.13}+\frac{1}{13.19}+\frac{1}{19.25}+\frac{1}{25.31}+\frac{1}{31.37}\)

\(6A=\frac{6}{1.7}+\frac{6}{7.13}+\frac{6}{13.19}+\frac{6}{19.25}+\frac{6}{25.31}+\frac{6}{31.37}\)

\(=1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+\frac{1}{13}-\frac{1}{19}+\frac{1}{19}-\frac{1}{25}+\frac{1}{25}-\frac{1}{31}+\frac{1}{31}-\frac{1}{37}\)

\(=1-\frac{1}{37}=\frac{36}{37}\)

\(A=\frac{6}{37}\)

\(\frac{1}{7}+\frac{1}{91}+\frac{1}{247}+\frac{1}{475}+\frac{1}{775}+\frac{1}{1147}\)

\(=\frac{1}{1\cdot7}+\frac{1}{7\cdot13}+\frac{1}{13\cdot19}+...+\frac{1}{31\cdot37}\)

\(=\frac{1}{6}\left(\frac{6}{1\cdot7}+\frac{6}{7\cdot13}+\frac{6}{13\cdot19}+...+\frac{6}{31\cdot37}\right)\)

\(=\frac{1}{6}\left(1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+\frac{1}{13}-\frac{1}{19}+...-\frac{1}{31}-\frac{1}{37}\right)\)

\(=\frac{1}{6}\left(1-\frac{1}{37}\right)\)

\(=\frac{1}{6}\cdot\frac{36}{37}=\frac{6}{37}\)

Tổng cần tính bằng:\(\frac{1}{1.7}\)+\(\frac{1}{7.13}\)+\(\frac{1}{13.19}\)+\(\frac{1}{19.25}\)+\(\frac{1}{25.31}\)+\(\frac{1}{31.37}\)=(\(\frac{1}{1}\)-\(\frac{1}{7}\)+\(\frac{1}{7}\)-\(\frac{1}{13}\)+...+\(\frac{1}{31}\)\(\frac{1}{37}\)):3 =(\(1\)-\(\frac{1}{37}\)):3=\(\frac{12}{37}\)

\(\frac{12}{37}\)kà kết quả nha bạn. chúc bạn học tốt. ( kik mình nha)

A=1/7 +1/91 +1/247 + 1/475 + 1/775 + 1/1147

A=1/(1.7)+1/(7.13)+1/(13.19)+...+1/(31...  

A=(1/6)*( 1 - 1/7 + 1/7 - 1/13 +... +1/31-1/37)  

A=(1/6)*(1-1/37)  

A=(1/6)*(36/37)  

A=6/37 

\(\frac{-1}{91}+\frac{-1}{247}+\frac{-1}{475}+\frac{-1}{775}+\frac{-1}{1147}\)

\(=-\left(\frac{1}{7.13}+\frac{1}{13.19}+\frac{1}{19.25}+\frac{1}{25.31}+\frac{1}{31.37}\right)\)

\(=-[\frac{1}{6}.\left(\frac{6}{7.13}+\frac{6}{13.19}+\frac{6}{19.25}+\frac{6}{25.31}+\frac{6}{31.37}\right)]\)

\(=-\text{[}\frac{1}{6}.\left(\frac{1}{7}-\frac{1}{13}+\frac{1}{13}-\frac{1}{19}+\frac{1}{19}-\frac{1}{25}+\frac{1}{25}-\frac{1}{31}+\frac{1}{31}-\frac{1}{37}\right)\text{]}\)

\(=-\text{[}\frac{1}{6}.\left(\frac{1}{7}-\frac{1}{37}\right)\text{]}\)

\(=-\text{[}\frac{1}{6}.\frac{30}{259}\text{]}\)

\(=-\frac{5}{259}\)

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

Ta có:

\(74\frac{19}{35}.\frac{7}{90}+15\frac{16}{35}:\frac{90}{7}\)

\(=74\frac{19}{35}.\frac{7}{90}+15\frac{16}{35}.\frac{7}{90}\)

\(=\frac{7}{90}.\left(74\frac{19}{35}+15\frac{16}{35}\right)\)

\(=\frac{7}{90}.90\)

\(=7\)

\(74\frac{19}{35}.\frac{7}{90}+15\frac{16}{35}.\frac{7}{90}\)

\(\frac{7}{90}.\left(74\frac{19}{35}+15\frac{16}{35}\right)\)

\(\frac{7}{90}.90\)

\(7\)

=74\(\frac{19}{35}\).\(\frac{7}{90}\)+15\(\frac{16}{35}\).\(\frac{7}{90}\)

=(74\(\frac{19}{35}\)+15\(\frac{16}{35}\)).\(\frac{7}{90}\)

=90.\(\frac{7}{90}\)

=7

k cho mình nhé

dung 100%