Tính nhanh
1/6+1/12+1/20+...+1/90+1/110 (dạng đủ)
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VD
14
31 tháng 1 2016
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+..........+\frac{1}{132}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+..........+\frac{1}{11.12}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...........+\frac{1}{11}-\frac{1}{12}\)
\(=1-\frac{1}{12}\)
\(=\frac{11}{12}\)
5 tháng 7 2020
Bài làm
\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{90}+\frac{1}{110}\)
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{9.10}+\frac{1}{10.11}\)
\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)
\(A=\frac{1}{1}-\frac{1}{11}\)
\(A=\frac{10}{11}\)
IK
3
3 tháng 8 2017
\(\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{10.11}\)
=\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-......+\frac{1}{10}-\frac{1}{11}.\)
=\(\frac{1}{2}-\frac{1}{11}\)
=\(\frac{9}{22}.\)
PN
2
25 tháng 5 2016
1/12+1/20+1/30+...+1/90+1/110
=1/3.4+1/4.5+1/5.6+...+1/9.10+1/10.11
=1/3-1/4+1/4-1/5+1/5-1/6+...+1/9-1/10+1/10-1/11
=1/3-1/11
=8/33
6 tháng 8 2016
1/12+1/20+1/30+...+1/90+1/110
=1/3.4+1/4.5+1/5.6+...+1/9.10+1/10.11
=1/3-1/4+1/4-1/5+1/5-1/6+...+1/9-1/10+1/10-1/11
=1/3-1/11
=8/33
NA
1
18 tháng 9 2015
Đặt tổng trân là A
Ta có A=1/2x3+1/3x4+...+1/10x11
A=1/2-1/3+1/3-1/4+...+1/10-1/11
Sau khi rút gọn ta được A=1/2-1/11
A=9/22
NQ
3
DQ
2
25 tháng 7 2017
ta có:
1/6+1/12+1/20+1/30+.........+1/90+1/110
= 1/2x3+1/3x4+1/4x5+1/5x6+....+1/9x10+1/10x11
= 1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+....+1/9-1/10+1/10-1/11
=1/2-1/11=11/22-2/22=9/22
25 tháng 7 2017
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}\)
\(=\left(\frac{1}{2}-\frac{1}{11}\right)+\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{1}{4}-\frac{1}{4}\right)+...+\left(\frac{1}{10}-\frac{1}{10}\right)\)
\(=\frac{1}{2}-\frac{1}{11}=\frac{11}{22}-\frac{2}{22}=\frac{9}{22}\)
23 tháng 8 2017
\(\frac{1}{2}\) + \(\frac{1}{6}\) + \(\frac{1}{12}\) + ............ + \(\frac{1}{90}\) + \(\frac{1}{110}\)
= \(\frac{1}{1.2}\) + \(\frac{1}{2.3}\) + \(\frac{1}{3.4}\) + ............ + \(\frac{1}{9.10}\) + \(\frac{1}{10.11}\)
= 1 - \(\frac{1}{2}\) + \(\frac{1}{2}\) - \(\frac{1}{3}\) + \(\frac{1}{3}\) - \(\frac{1}{4}\) + ................. + \(\frac{1}{9}\) - \(\frac{1}{10}\) + \(\frac{1}{10}\) - \(\frac{1}{11}\)
= 1 - \(\frac{1}{11}\)
= \(\frac{10}{11}\)
AM
2
DD
8 tháng 8 2015
\(A=\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...+\frac{1}{10}-\frac{1}{11}=\frac{1}{2}-\frac{1}{11}=\frac{9}{22}\)
8 tháng 8 2015
=1/2.3+1/3.4+1/4.5+......+1/10.11
=1-1/2+1/2-1/3+.....,+1/10-1/11
=1-1/11
=10/11
Tick
\(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{90}+\dfrac{1}{110}\)
\(=\dfrac{1}{2x3}+\dfrac{1}{3x4}+\dfrac{1}{4x5}+...+\dfrac{1}{9x10}+\dfrac{1}{10x11}\)
\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{11}\)
\(=\dfrac{1}{2}-\dfrac{1}{11}=\dfrac{11}{22}-\dfrac{2}{22}=\dfrac{9}{22}\)
1/6+1/12+1/20+1/90+1/110
=1/2x3+1/3x4+1/4x5+...+1/9x10+1/10x11
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-...+1/9-1/10+1/10-1/11
=1/2-1/11=9/22