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!

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

-.-

#)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

=335510

335510

\(B=1+\frac{3}{5}+\frac{3}{35}+\frac{3}{55}+.....+\frac{3}{9999}\)

\(B=\frac{3}{1}.3+\frac{3}{3}.5+\frac{3}{5}.7+......+\frac{3}{99}.101\)

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

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

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

\(B=\frac{3}{2}.\frac{100}{101}\)

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

bạn tách ra xong làm cx dễ mà đây là toán 6

Cảm ơn câu trả lời thật súc tích và thật ngắn gọn của bạn

\(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{48.49.50}\)

\(A=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{48.49}-\frac{1}{49.50}\right)\)
\(A=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{49.50}\right)\)

\(A=\frac{1}{2}.\frac{612}{1225}=\frac{306}{1225}\)

~ Hok tốt ~

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

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

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

Ta có:

\(A=\frac{1}{358}.\left(7+\frac{1}{297}\right)-\left(4-\frac{1}{358}\right).2.\frac{1}{297}-7.\frac{1}{358}-\frac{3}{297}.\frac{1}{358}\)

\(=\frac{1}{358}.\left(7+\frac{1}{297}-7-\frac{3}{297}\right)-\left(4-\frac{1}{358}\right).\frac{2}{297}\)

\(=\frac{1}{358}.\left(-\frac{2}{297}\right)-\frac{2}{297}.\left(4-\frac{1}{358}\right)\)

\(=\left(-\frac{2}{297}\right)\left(\frac{1}{358}+4-\frac{1}{358}\right)\)

\(=\left(-\frac{2}{297}\right)\left(-4\right)\)

\(=\frac{8}{297}\)

Vậy giá trị biểu thức A là \(\frac{8}{297}\)