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1/5*7 + 1/7*9 + 1/9*11 + ... + 1/13*15
= 1/2(2/5*7 + 2/7*9 + 2/9*11 + ... + 2/13*15)
= 1/2(1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11 + 1/11 - 1/13 + 1/13 - 1/15)
= 1/2(1/5 - 1/15)
= 1/2.2/15
= 1/15
Bài giải
\(\text{Đặt }A=\frac{1}{5\text{ x }7}+\frac{1}{7\text{ x }9}+\frac{1}{9\text{ x }11}+\frac{1}{11\text{ x }13}+\frac{1}{13\text{ x }15}\)
\(A=\frac{1}{2}\left(\frac{2}{5\text{ x }7}+\frac{2}{7\text{ x }9}+\frac{2}{9\text{ x }11}+\frac{2}{11\text{ x }13}+\frac{2}{13\text{ x }15}\right)\)
\(A=\frac{1}{2}\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)
\(A=\frac{1}{2}\left(\frac{1}{5}-\frac{1}{15}\right)\)
\(A=\frac{1}{2}\cdot\frac{2}{15}\)
\(A=\frac{1}{15}\)
\(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.........+\frac{1}{13}-\frac{1}{15}\)
\(=1-\frac{1}{15}\)
\(=\frac{14}{15}\)
\(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}+\frac{2}{11\cdot13}+\frac{2}{13\cdot15}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\)
\(=\frac{1}{3}-\frac{1}{15}\)
\(=\frac{4}{15}\)
Chúc bn hok giỏi !!!!!!!!! ^_^
S=1/5-1/7+1/7-1/9+1/9-1/11+...+1/93-1/95
S=1/5-1/95
S=18/95
Đặt \(A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\)
\(2A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\)
\(2A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)
\(2A=1-\frac{1}{9.11}=1-\frac{1}{99}=\frac{98}{99}\)
\(A=\frac{98}{99}:2=\frac{49}{99}\)
Ủng hộ mk nha!!!
A = \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\)
A = \(\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)
A = \(\frac{1}{2}.\left(1-\frac{1}{11}\right)=\frac{1}{2}.\frac{10}{11}\)
A = \(\frac{5}{11}\)
\(\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\right)y=\frac{2}{3}\)
=> \(\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)y=\frac{2}{3}\)
=> \(\frac{1}{2}\left(1-\frac{1}{11}\right)y=\frac{2}{3}\)
=> \(\frac{1}{2}.\frac{10}{11}y=\frac{2}{3}\)
=> \(\frac{5}{11}y=\frac{2}{3}\)
=>y = \(\frac{2}{3}:\frac{5}{11}\)
=> y = \(\frac{22}{15}\)
cho mk cái lời giải thích chỗ nhân 1/2 ý mk ko hiểu mong bn thông cảm
Giải:
\(\left(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+\dfrac{1}{7.9}+\dfrac{1}{9.11}\right)y=-\dfrac{2}{3}\)
\(\Leftrightarrow\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+\dfrac{1}{7.9}+\dfrac{1}{9.11}=-\dfrac{2}{3y}\)
\(\Leftrightarrow\dfrac{1}{2}\left(\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}\right)=-\dfrac{2}{3y}\)
\(\Leftrightarrow\dfrac{1}{2}\left(\dfrac{1}{1}-\dfrac{1}{11}\right)=-\dfrac{2}{3y}\)
\(\Leftrightarrow\dfrac{1}{2}.\dfrac{10}{11}=-\dfrac{2}{3y}\)
\(\Leftrightarrow\dfrac{5}{11}=-\dfrac{2}{3y}\)
\(\Leftrightarrow15y=-22\)
\(\Leftrightarrow y=-\dfrac{22}{15}\)
Vậy ...
Lời giải:
$6C=5\times 7\times (9-3)+7\times 9\times (11-5)+9\times 11\times (13-7)+....+199\times 201\times (203-197)$
$=(5\times 7\times 9+7\times 9\times 11+9\times 11\times 13+...+199\times 201\times 203)-(3\times 5\times 7+5\times 7\times 9+....+197\times 199\times 201)$
$=199\times 201\times 203-3\times 5\times 7$
$=8119692$
$\Rightarrow C=1353282$