tính tổng:
Q= 1/3.5 + 1/5.7+ 1/9.7+...........+1/2013.2015.
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\(B=\frac{1}{1\times3}+\frac{1}{3\times5}+\frac{1}{5\times7}+...+\frac{1}{2013\times2015}\\
2B=\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{2013\times2015}\\
2B=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2013}-\frac{1}{2015}\\2B=1-\frac{1}{2015}=\frac{2014}{2015}\\
\Rightarrow B=\frac{2014}{2015}
\div2=\frac{1007}{2015}\)
\(A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+.....+\frac{1}{2013.2015}\)
\(=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+......+\frac{2}{2013.2015}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{2013}-\frac{1}{2015}\right)\)
\(=\frac{1}{2}.\left(1-\frac{1}{2015}\right)=\frac{1}{2}.\frac{2014}{2015}=\frac{1007}{2015}\)
Vậy A=1007/2015
\(2A=2\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{2013.2015}\right)\)
\(2A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2013}-\frac{1}{2015}\)
\(2A=1-\frac{1}{2015}\)
\(A=\frac{2014}{2015}:2\)
\(A=\frac{1007}{2015}\)
1/1.3+1/3.5+...+1/2013.2015
=1/2.(1/1-1/3+1/3-1/5+...+1/2013-1/2015)
=1/2.(1/1-1/2015)
=1/2.2014/2015
=1007/2015
A=1/1.3+1/3.5+1/5.7+...+1/2013.2015
2A=2.(1/1.3+1/3.5+1/5.7+...+1/2013.2015)
=2/1.3+2/3.5+2/5.7+...+2/2013.2015
=1-1/3+1/5-1/7+1/7-1/9+...+1/2013-1/2015
=1-1/2015
=2014/2015
=>2A=2014/2015=>A=1007/2015
Q = \(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2013.2015}\)
Q = \(\frac{1}{2}.\left(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{1}{2013.2015}\right)\)
Q = \(\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{2015}\right)\)
Q = \(\frac{1}{2}.\frac{2012}{6045}=\frac{1002}{6045}\)
\(Q=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{2013.2015}\)
\(\Rightarrow Q.2=2.\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{2013.2015}\right)\)
\(\Rightarrow Q.2=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{2013.2015}\)
\(\Rightarrow Q.2=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{2013}-\frac{1}{2015}\)
\(\Rightarrow Q.2=\frac{1}{3}-\frac{1}{2015}\)
\(\Rightarrow Q.2=\frac{2012}{6045}\)
\(\Rightarrow Q=\frac{2012}{6045}.\frac{1}{2}=\frac{1006}{6045}\)
Mk tinh nhẩm, nên ko bt kết quả có đúng ko
nên bn thử tính lại kết quả nha!!!
Chúc bn hok tốt!!!
\(=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{2015}\right)=\frac{1}{2}.\frac{2012}{6045}=\frac{1006}{6045}\)
lm tắt cu~g chả bt đúng ko ^^, thông cảm
A= 1/1.3+1/3.5+1/5.7+.....+1/2013.2015
2A=2/1.3+2/3.5+2/5.7+......+2/2013.2015
A=1/1-1/3+1/3-1/5+1/5-1/7+....+1/2013-1/2015
A=1-1/2015=2014/2015
=>A=2014/2015:2
=>A=2014/4030
I K MK MK K LI 3 K
\(M=1-\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{2013.2015}\right)\)
\(M=1-\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{2013.2015}\right)\)
\(M=1-\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2013}-\frac{1}{2015}\right)\)
\(M=1-\frac{1}{2}.\left(1-\frac{1}{2015}\right)\)
bạn tự tính nốt nhé
\(M=1-\frac{1}{1.3}-\frac{1}{3.5}-\frac{1}{5.7}-...-\frac{1}{2013.2015}\)
\(\Leftrightarrow M=1-\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2013.2015}\right)\)
\(\Leftrightarrow M=1-\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2013.2015}\right)\)
\(\Leftrightarrow M=1-\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2013}-\frac{1}{2015}\right)\)
\(\Leftrightarrow M=1-\frac{1}{2}\left(1-\frac{1}{2015}\right)\)
\(\Leftrightarrow M=1-\frac{1}{2}.\frac{2014}{2015}\)
\(\Leftrightarrow M=1-\frac{2014}{4030}\)
\(\Leftrightarrow M=\frac{2016}{4030}=\frac{1008}{2015}\)
= 1/2. ( 1 - 1/3 + 1/3 - 1/5 + 1/5 -1/7 +........+ 1/2013 - 1/2015)
= 1/2 . ( 1- 1/2015)
= 1007/2015
Ta có: A=\(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+....+\dfrac{1}{2013.2015}\)
\(\Leftrightarrow2A=2\left(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{2013.2015}\right)\)
\(\Leftrightarrow2A=\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{2021}-\dfrac{1}{2013}+\dfrac{1}{2013}-\dfrac{1}{2015}\)
\(\Leftrightarrow2A=\dfrac{1}{3}-\dfrac{1}{2015}=\dfrac{2012}{6045}\)
\(\Leftrightarrow A=\dfrac{1006}{6045}\)
2A=\(\dfrac{2}{1.3}+\dfrac{2}{3.5}+...+\dfrac{1}{2013.2015}\)
2A=\(\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{2013}+\dfrac{1}{2015}\)
2A=\(\dfrac{1}{1}-\dfrac{1}{2015}\)
2A=\(\dfrac{2014}{2015}\)
A=\(\dfrac{1007}{2015}\)
Khi gặp bài này, bn nên tách 1 phân số ra thành hiệu của 2 phân số.
Q= 1/3.5 + 1/5.7+ 1/9.7+...........+1/2013.2015.
Q = 1/2 . 2 . ﴾ 1/3.5+1/5.7+1/7.9+1/9.11 +........+1/2013.2015﴿
Q = 1/2 . ﴾2/3.5 + 2/5.7+2/7.9+2/9.11+.......+2/2013.2015﴿
Q = 1/2 . [1/3+ ﴾‐1/5 + 1/5﴿ + ﴾‐1/7+1/7﴿+ ﴾‐1/9 + 1/9﴿+ ‐1/11 +......+1/2013 + ‐ 1/2015]
Q= 1/2 . ﴾ 1/3 + ‐1/2015 ﴿
Q = 1/2 . 2012/6045 = 1006/6045.
=> Q = 1006 / 6045
k nhé
\(2Q=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2013}-\frac{1}{2015}\)
\(2Q=\frac{1}{3}-\frac{1}{2015}\)
\(2Q=\frac{2012}{6045}\)
\(Q=\frac{1006}{6045}\)