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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
\(S=\frac{1}{9}+\frac{1}{45}+\frac{1}{105}+\frac{1}{189}+\frac{1}{297}\)
\(S=\frac{1}{1.9}+\frac{1}{9.5}+\frac{1}{5.21}+\frac{1}{21.9}+\frac{1}{9.33}\)
\(5S=\frac{5}{1.9}+\frac{5}{9.5}+\frac{5}{5.21}+\frac{5}{21.9}+\frac{5}{9.33}\)
\(5S=1-\frac{1}{9}+\frac{1}{9}-\frac{1}{5}+\frac{1}{5}+\frac{1}{21}+\frac{1}{21}-\frac{1}{9}+\frac{1}{9}-\frac{1}{33}\)
\(5S=1-\frac{1}{33}\)
\(5S=\frac{32}{33}\)
\(S=\frac{32}{33}:5\)
\(S=\frac{32}{165}\)
#)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+\(\frac{3}{5}\)+\(\frac{14}{15}\).
=\(\frac{8}{5}\)+\(\frac{14}{15}\).
=\(\frac{15}{38}\)
\(A=\frac{7}{9}+\frac{7}{45}+\frac{7}{105}+...+\frac{7}{27645}\)
\(=7\left(\frac{1}{9}+\frac{1}{45}+\frac{1}{105}+...+\frac{1}{27645}\right)\)
\(=7.\frac{1}{3}\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+...+\frac{1}{9215}\right)\)
\(=\frac{7}{3}\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{95.97}\right)\)
Đặt \(S=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{95.97}\)
\(2S=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{95.97}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{95}-\frac{1}{97}\)
\(=1-\frac{1}{97}=\frac{96}{97}\)
\(\Rightarrow S=\frac{96}{97}:2=\frac{96}{97.2}=\frac{48}{97}\). Thay vào \(A\) ta có:
\(A=\frac{7}{3}.\frac{48}{97}=\frac{112}{97}\)
Vậy \(A=\frac{112}{97}\).
-6/18 + 10/18 + 3/18 < x < 95/45 + 9/45 + 2/45
4/18 + 3/18 < x < 104/45 + 2/45
7/18 < x < 106/45
10/45 < x < 106/45
Vậy x = 11/45,12/45,13/45,.......,105/45
\(M=\frac{\left(-7\right).15.9.15.14}{9.49.7.15}=\frac{-15.2}{7}=\frac{-30}{7}.\)
\(N=\frac{200}{189}+\frac{1}{14}=\)1.12962962963
\(M=\left(\frac{-7}{9}\cdot\frac{9}{7}\right)\cdot\left(\frac{15}{49}\cdot\frac{14}{15}\right)\cdot15\)
\(M=\left(-1\right)\cdot\frac{2}{7}\cdot15\)
\(M=\frac{-30}{7}\)
\(N=\frac{5}{9}\cdot\frac{4}{7}\cdot\frac{10}{3}+\frac{3}{9}\cdot\frac{3}{7}\cdot\frac{1}{2}\)
\(N=\frac{200\cdot2}{189\cdot2}+\frac{9\cdot3}{126\cdot3}\)
\(N=\frac{400}{378}+\frac{27}{378}\)
\(N=\frac{61}{51}\)
T i ck nha
#)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
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