Tính B = \(\frac{3}{2x5}+\frac{3}{5x8}+\frac{3}{8x11}+\frac{3}{11x14}\)
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26 tháng 5 2018
\(\frac{1}{2\times5}+\frac{1}{5\times8}+\frac{1}{8\times11}+\frac{1}{11\times14}+\frac{1}{14\times17}+\frac{1}{17\times20}\)
\(=\frac{1}{3}\times\left(\frac{3}{2\times5}+\frac{3}{5\times8}+\frac{3}{8\times11}+\frac{3}{11\times14}+\frac{3}{14\times17}+\frac{3}{17\times20}\right)\)
\(=\frac{1}{3}\times\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+\frac{1}{17}-\frac{1}{20}\right)\)
\(=\frac{1}{3}\times\left(\frac{1}{2}-\frac{1}{20}\right)\)
\(=\frac{1}{3}\times\frac{9}{20}\)
\(=\frac{3}{20}\)
_Chúc bạn học tốt_
26 tháng 5 2018
Đặt \(A=\frac{1}{2x5}+\frac{1}{5x8}+..+\frac{1}{17x20}\)
\(3xA=3x\left(\frac{1}{2x5}+\frac{1}{5x8}+...+\frac{1}{17x20}\right)\)
\(3xA=\frac{3}{2x5}+\frac{3}{5x8}+....+\frac{3}{17x20}\)
\(3xA=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+..+\frac{1}{17}-\frac{1}{20}\)
\(3xA=\frac{1}{2}-\frac{1}{20}\)
\(3xA=\frac{9}{20}\)
\(\Rightarrow A=\frac{3}{20}\)
TH
1
23 tháng 3 2023
Ta có : A=3/2x5+3/5x8+3/8x11+3/11x14+3/14x17+3/17x20
=> A=1/2-1/5+1/5-1/8+1/8-1/11+1/11-1/14+1/14-1/17+1/17-1/20
=> A=1/2-1/20
=> A=9/20
Vậy A=9/20
đó
16 tháng 8 2017
= 5-2/2x5+8-5/5x8+11-8/8x11+14-11/11x14
=(1/2-1/5)+(1/5-1/8)+(1/8-1/11)+(1/11-1/14)
=(1/2+1/5+1/8+1/11)-(1/5+1/8+1/11+1/14)
=1/2-1/14
=3/7
Vậy B=3/7
NG
2
27 tháng 1 2016
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VT
28 tháng 3 2022
A = \(\dfrac{1}{2}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{8}\) + \(\dfrac{1}{8}\) - \(\dfrac{1}{11}\) + \(\dfrac{1}{11}\) - \(\dfrac{1}{14}\) + \(\dfrac{1}{14}\) - \(\dfrac{1}{17}\) + \(\dfrac{1}{17}\) - \(\dfrac{1}{20}\)
= \(\dfrac{1}{2}\) - \(\dfrac{1}{20}\)
= \(\dfrac{9}{20}\)
25 tháng 7 2017
= 2 x ( 1/2 x 5 + 1/ 5 x 8 + 1/ 8 x 11 + 1/ 11 x 14 + 1/ 14 x 17 )
= 2 x ( 1/2 - 1/5 + 1/5 - 1/8 + ....+1/14 - 1/17)
= 2 x (1/2 - 1/17)
= 2 x 15/34
= 15/17
ĐÚNG THÌ TÍCH CHO MÌNH NHA
CHÚC BẠN HỌC GIỎI
DP
25 tháng 7 2017
Đặt \(A=\frac{2}{2.5}+\frac{2}{5.8}+\frac{2}{8.11}+\frac{2}{11.14}+\frac{2}{14.17}\)
\(A=\frac{2}{3}\cdot\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{14}-\frac{1}{17}\right)\)
\(A=\frac{2}{3}\cdot\left(\frac{1}{2}-\frac{1}{17}\right)\)
\(A=\frac{2}{3}\cdot\frac{15}{34}=\frac{5}{17}\Rightarrow A< 1\)
\(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}\)
\(=\frac{1}{2}-\frac{1}{14}\)
\(=\frac{7}{14}-\frac{1}{14}\)
\(=\frac{6}{14}\)
\(=\frac{3}{7}\)
3/2x5 + 3/5x8 + 3/8x11 + 3/11x14
= 3/2 - 3/5 + 3/5 - 3/8 + 3/8 - 3/11 + 3/11 - 3/14
= 3/2 - 3/14
= 21/14 - 3/14
= 18/14
= 9/5