a) -90/189 + 45/84 - 78/126

= -10/21 + 15/28 - 13/21

= (-10/21 - 13/21) + 15/28

= -24/21 + 15/28

= -17/28

\(\frac{90}{60}-\frac{189}{126}=\frac{3}{2}-\frac{3}{2}=0\)

\(\frac{90}{60}-\frac{189}{126}=\frac{3}{2}-\frac{3}{2}=0\)

\(\frac{90}{60}-\frac{189}{126}=\frac{3}{2}-\frac{3}{2}=0\)

#)Giải :

\(\frac{1}{15}+\frac{4}{30}+\frac{9}{45}+\frac{16}{60}+...+\frac{81}{135}=\frac{1}{15}+\frac{2}{15}+\frac{3}{15}+...+\frac{9}{15}=\frac{45}{15}=3\)

Dễ ẹc ak :v rút gọn là ra

=(\(\frac{1}{15}\)+\(\frac{4}{30}\)+\(\frac{16}{60}\)+\(\frac{64}{120}\))+(\(\frac{9}{45}\)+\(\frac{36}{90}\))+(\(\frac{25}{75}\)+\(\frac{81}{135}\))

=(\(\frac{8}{120}\)+\(\frac{16}{120}\)+\(\frac{32}{120}\)+\(\frac{64}{120}\))+(\(\frac{18}{90}\)+\(\frac{36}{90}\))+\(\frac{14}{15}\).

=1+\(\frac{3}{5}\)+\(\frac{14}{15}\).

=\(\frac{8}{5}\)+\(\frac{14}{15}\).

=\(\frac{15}{38}\)

a)     5/30+15/90+25/150+35/210+45/270

       =1/6+1/6+1/6+1/6+1/6

       =1/6 x 5

       =5/6

b)     1/2+1/6+1/12+1/20+....+1/56

        =1/1x2+1/2x3+1/3x4+1/4x5+.....1/7x8

        =1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.......-1/7+1/7-1/8

        =1/1-1/8

         =7/8

c)     mình chịu

thank you bn nhìu nha

chịu,khó quá,nhất là câu c ý

#)Giải :

\(P=1+\frac{9}{45}+\frac{9}{105}+\frac{9}{189}+...+\frac{9}{29997}\)

\(P=\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+...+\frac{3}{99.101}\)

\(P=\frac{3}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101} \right)\)

\(P=\frac{3}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(P=\frac{3}{2}\left(1-\frac{1}{101}\right)\)

\(P=\frac{3}{2}\times\frac{100}{101}\)

\(P=\frac{150}{101}\)

trả lời 

=150/101 

chúc bn 

hc tốt

trả lời 

=150/101

chúc bn 

hc tốt

S = 1/9 + 1/45 + 1/105 + 1/189 + 1/297

=> S = 1/2 ( 6/27 + 6/135 + 6/315 + 6/567 + 6/891 )

=> S = 1/2 ( 6/3.9 + 6/9.15 + 6/15.21 + 6/21.27 + 6/27.33 )

=> S = 1/2 ( 1/3 - 1/9 + 1/9 - 1/15 + ... + 1/27 - 1/33 )

=> S = 1/2 ( 1/3 - 1/33 )

=> S = 1/2 . 10/33

=> S = 5/33

\(S=\frac{1}{9}+\frac{1}{45}+\frac{1}{105}+\frac{1}{189}+\frac{1}{297}\)

\(S=\frac{1}{1.9}+\frac{1}{9.5}+\frac{1}{5.21}+\frac{1}{21.9}+\frac{1}{9.33}\)

\(5S=\frac{5}{1.9}+\frac{5}{9.5}+\frac{5}{5.21}+\frac{5}{21.9}+\frac{5}{9.33}\)

\(5S=1-\frac{1}{9}+\frac{1}{9}-\frac{1}{5}+\frac{1}{5}+\frac{1}{21}+\frac{1}{21}-\frac{1}{9}+\frac{1}{9}-\frac{1}{33}\)

\(5S=1-\frac{1}{33}\)

\(5S=\frac{32}{33}\)

\(S=\frac{32}{33}:5\)

\(S=\frac{32}{165}\)

Cậu Bé Tiến Pro sai rồi nhé!

\(\frac{5}{1.9}=1-\frac{1}{9}\Leftrightarrow9-1=5\)

-.-

S+..... 

là sao vậy ??

S = NHA

\(=\frac{5}{33}\)

@@@@@@@@@@@

~ học tốt ~

Máy tính bấm auto ra ... =))

\(A=\frac{1}{18}+\frac{1}{36}+\frac{1}{60}+...+\frac{1}{168}\)

 \(\frac{1}{3}A=\frac{1}{54}+\frac{1}{108}+...+\frac{1}{504}\)

\(\frac{1}{3}A=\frac{1}{6.9}+\frac{1}{9.12}+...+\frac{1}{21.24}\)

\(=\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+...+\frac{1}{21}-\frac{1}{24}\)

\(=\frac{1}{6}-\frac{1}{24}\)

\(=\frac{4-1}{24}=\frac{3}{24}=\frac{1}{8}\)

=> \(A=\frac{1}{8}:\frac{1}{3}\)\(=\frac{3}{8}\)