4/1x3+4/3x5+4/5x7+...+4/2009x2011
K
Khách
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28 tháng 7 2015
2/1.3 + 2/3.5 + 2/5.7 + ... + 2/2009.2011
= 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/2009 - 1/2011
= 1 - 1/2011
= 2010/2011
NT
1
YG
15 tháng 5 2016
A = 1/1x3 + 1/3x5 + 1/5x7 +.........+ 1/2009x2011
= 1/1-1 +1/3-5 + 1/5-7 + .......+ 1/2009-2011
= 1/1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 +........+ 1/2009 -1/2011
= 1/1 - 1/2011
= 2010/2011
HV
4
7 tháng 3 2018
Ta có;\(\frac{4}{1\times3}+\frac{4}{3\times5}+\frac{4}{5\times7}+....+\frac{4}{19\times21}\)
\(=2\times\left(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+....+\frac{2}{19\times21}\right)\)
\(=2\times\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}\right)\)
\(=2\times\left(1-\frac{1}{21}\right)=2\times\frac{20}{21}=\frac{40}{21}\)
AK
7 tháng 3 2018
4/1 x 3 + 4/ 3 x 5 + 4/ 5 x 7 + ....+ 4/ 17 x 19 + 4/ 19 x 21
= 2 x ( 2/ 1 x 3 + 2/ 3 x 5 + 2/ 5 x 7 + ...+ 2/ 17 x 19 + 2/ 19 x 21 )
= 2 x ( 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ...+ 1/17 - 1/19 + 1/19 - 1/21 )
= 2 x ( 1 - 1/21 )
= 2 x 20/21
= 40/21
Chúc bạn học giỏi !!!
LB
1
AH
Akai Haruma
Giáo viên
12 tháng 8 2023
Lời giải:
Gọi tổng trên là $A$
$A=2\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{25.27}\right)$
$=2\left(\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+...+\frac{27-25}{25.27}\right)$
$=2\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{25}-\frac{1}{27}\right)$
$=2\left(1-\frac{1}{27})=\frac{52}{27}$
7 tháng 10 2021
\(K=\dfrac{4}{1\times3}+\dfrac{4}{3\times5}+...+\dfrac{4}{299\times301}\)
\(=2\times\left(\dfrac{2}{1\times3}+\dfrac{2}{3\times5}+...+\dfrac{2}{299\times301}\right)\)
\(=2\times\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{299}-\dfrac{1}{301}\right)\)
\(=2\times\left(1-\dfrac{1}{301}\right)=2\times\dfrac{300}{301}=\dfrac{600}{301}\)
7 tháng 10 2021
\(K=\dfrac{4}{1\cdot3}+\dfrac{4}{3\cdot5}+...+\dfrac{4}{299\cdot301}\)
\(=2\left(\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{299}-\dfrac{1}{301}\right)\)
\(=2\cdot\dfrac{300}{301}=\dfrac{600}{301}\)
PT
2
20 tháng 12 2015
a=1/1x2+1/2x3+....+1/99x100
a=1-1/2+1/2-1/3+....+1/99-1/100
a=1-1/100
a=99/100
b=4/1x3+4/3x5+.....+4/51x53
b=2x(2/1x3+2/3x5+....+2/51x53)
b=2x(1-1/3+1/3-1/5+...+1/51-1/53)
b=2x(1-1/53)
b=2x52/53
b=104/53
đúng tick cho mình nha
NQ
2
NH
1 tháng 2 2020
\(S=\frac{4}{1\times3}+\frac{16}{3\times5}+\frac{36}{5\times7}+...+\frac{2500}{49\times51}\)
\(=\frac{1\times3+1}{1\times3}+\frac{3\times5+1}{3\times5}+\frac{5\times7+1}{5\times7}+...+\frac{49\times51+1}{49\times51}\)
\(=\frac{1\times3}{1\times3}+\frac{1}{1\times3}+\frac{3\times5}{3\times5}+\frac{1}{3\times5}+\frac{5\times7}{5\times7}+\frac{1}{5\times7}+...+\frac{49\times51}{49\times51}+\frac{1}{49\times51}\)
\(=1+\frac{1}{1\times3}+1+\frac{1}{3\times5}+1+\frac{1}{5\times7}+...+\frac{1}{49\times51}\) ( Có : \(\left(51-3\right)\div2+1=25\)chữ số 1 )
\(=25+\frac{1}{1\times3}+\frac{1}{3\times5}+\frac{1}{3\times5}+\frac{1}{5\times7}+...+\frac{1}{49\times51}\)
\(=25+\frac{1}{2}\times\left(1-\frac{1}{3}\right)+\frac{1}{2}\times\left(\frac{1}{3}-\frac{1}{5}\right)+\frac{1}{2}\times\left(\frac{1}{5}-\frac{1}{7}\right)+...+\frac{1}{2}\times\left(\frac{1}{49}-\frac{1}{51}\right)\)
\(=25+\frac{1}{2}\times\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{49}-\frac{1}{51}\right)\)
\(=25+\frac{1}{2}\times\left(1-\frac{1}{51}\right)\)
\(=25+\frac{1}{2}\times\frac{50}{51}\)
\(=25+\frac{25}{51}\)
\(=\frac{1300}{51}\)
1 tháng 2 2020
\(S=\frac{4}{1.3}+\frac{16}{3.5}+\frac{36}{5.7}+...+\frac{2500}{49.51}\)
\(=\frac{4}{3}+\frac{16}{15}+\frac{36}{35}+...+\frac{2500}{2499}\)
\(=1+\frac{1}{3}+1+\frac{1}{15}+1+\frac{1}{35}+...+1+\frac{1}{2499}\)
\(=\left(1+1+1+...+1\right)+\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+...+\frac{1}{2500}\right)\)
\(=25+\left(\frac{1}{3}+\frac{1}{5}+\frac{1}{35}+...+\frac{1}{2499}\right)\)
Đặt \(A=\frac{1}{3}+\frac{1}{5}+\frac{1}{35}+...+\frac{1}{2499}\)
\(=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{49.51}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{49}-\frac{1}{51}\)
\(=1-\frac{1}{51}=\frac{50}{51}\)
\(\Rightarrow S=25+\frac{50}{51}=\frac{1325}{51}\)
Vậy S=\(\frac{1325}{51}\)
VH
0
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
13 tháng 8 2023
Bài 1:
A = \(\dfrac{1}{1\times3}\) + \(\dfrac{1}{3\times5}\) + \(\dfrac{1}{5\times7}\) +...+ \(\dfrac{1}{2019\times2021}\)
A = \(\dfrac{1}{2}\) \(\times\) ( \(\dfrac{2}{1\times3}\) + \(\dfrac{2}{3\times5}\) + \(\dfrac{2}{5\times7}\)+...+ \(\dfrac{2}{2019\times2021}\))
A = \(\dfrac{1}{2}\) \(\times\)( \(\dfrac{1}{1}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{7}\)+...+ \(\dfrac{1}{2019}\) - \(\dfrac{1}{2021}\))
A = \(\dfrac{1}{2}\) \(\times\) ( \(\dfrac{1}{1}\) - \(\dfrac{1}{2021}\))
A = \(\dfrac{1010}{2021}\)