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23 tháng 8 2015
=1/4x5+1/5x6+1/6x7+...+1/9x10+1/10x11
=1/4-1/5+1/5-1/6+...+1/10-1/11
=1/4-1/11
=7/44
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
HP
8 tháng 5 2016
Tổng quát: \(\frac{1}{n\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}\)
\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+..+\frac{1}{110}=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+....+\frac{1}{10.11}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+....+\frac{1}{10}-\frac{1}{11}\)
\(=\frac{1}{2}-\frac{1}{11}=\frac{9}{22}\)
NM
2
28 tháng 6 2016
Ta có: \(\frac{1}{6}+\frac{1}{12}+....+\frac{1}{110}\)
\(\Rightarrow\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+.....+\frac{1}{10.11}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{10}-\frac{1}{11}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{11}=\frac{9}{22}\)
28 tháng 6 2016
\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+........+\frac{1}{110}\)
\(=\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+.......+\frac{1}{10\times11}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....+\frac{1}{10}-\frac{1}{11}\)
\(=\frac{1}{2}-\frac{1}{11}\)
\(=\frac{11}{22}-\frac{2}{22}\)
\(=\frac{9}{22}\)
NT
2
20 tháng 6 2016
\(B=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{90}+\frac{1}{110}\)
\(B=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{9.10}+\frac{1}{10.11}\)
\(B=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{9}-\frac{1}{10}\)\(+\frac{1}{10}-\frac{1}{11}\)
\(B=\frac{1}{2}-\frac{1}{11}\)
\(B=\frac{9}{22}\)
20 tháng 6 2016
Thôi chết! Ở hàng thứ 3 của bài Mình có ghi 1/2 - 1/3 + 1/3 - 1/4 +1/4 - 1/5 .... nha bạn! Không phải bằng đâu ^.^
PP
3
TH
Thầy Hùng Olm
Manager
VIP
4 tháng 6 2023
\(\dfrac{1}{20}=\dfrac{1}{4x5}=\dfrac{1}{4}-\dfrac{1}{5}\)
Tương tự các phân số khác
S= \(\dfrac{1}{4}-\dfrac{1}{12}=\dfrac{1}{6}\)
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
4 tháng 6 2023
\(\dfrac{1}{20}+\dfrac{1}{30}\)+ \(\dfrac{1}{42}\)+\(\dfrac{1}{56}\)+\(\dfrac{1}{72}\)+\(\dfrac{1}{90}\)+\(\dfrac{1}{110}\)+\(\dfrac{1}{132}\)
= \(\dfrac{1}{4\times5}\)+\(\dfrac{1}{5\times6}\)+\(\dfrac{1}{6\times7}\)+\(\dfrac{1}{7\times8}\)+\(\dfrac{1}{8\times9}\)+\(\dfrac{1}{9\times10}\)+\(\dfrac{1}{10\times11}\)+\(\dfrac{1}{11\times12}\)
= \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\)+\(\dfrac{1}{5}\)-\(\dfrac{1}{6}\)+\(\dfrac{1}{6}\)-\(\dfrac{1}{7}\)+\(\dfrac{1}{7}\)-\(\dfrac{1}{8}\)+\(\dfrac{1}{8}\)-\(\dfrac{1}{9}\)+\(\dfrac{1}{9}\)-\(\dfrac{1}{10}\)+\(\dfrac{1}{10}\)-\(\dfrac{1}{11}\)+\(\dfrac{1}{11}\)-\(\dfrac{1}{12}\)
= \(\dfrac{1}{4}\) - \(\dfrac{1}{12}\)
= \(\dfrac{3}{12}\) - \(\dfrac{1}{12}\)
= \(\dfrac{2}{12}\)
=\(\dfrac{1}{6}\)
NT
2
D
29 tháng 5 2022
`=1/[4xx5]+1/[5xx6]+1/[6xx7]+...+1/[11xx12]`
`=1/4-1/5+1/5-1/6+1/6-1/7+...+1/11-1/12`
`=1/4-1/12=3/12-1/12=2/12=1/6`
29 tháng 5 2022
\(\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}+\dfrac{1}{110}+\dfrac{1}{132}\\ =\dfrac{1}{4\times5}+\dfrac{1}{5\times6}+\dfrac{1}{6\times7}+\dfrac{1}{7\times8}+\dfrac{1}{8\times9}+\dfrac{1}{9\times10}+\dfrac{1}{10\times11}+\dfrac{1}{11\times12}\\ =\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}\\ =\dfrac{1}{4}-\dfrac{1}{12}\\ =\dfrac{3}{12}-\dfrac{1}{12}=\dfrac{2}{12}=\dfrac{1}{6}\)
MP
1
18 tháng 7 2015
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{90}+\frac{1}{110}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{9.10}+\frac{1}{10.11}\)
=\(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...\frac{1}{7}-\frac{1}{8}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)
\(=1-\frac{1}{8}+\frac{1}{9}-\frac{1}{11}\)
\(=\frac{709}{792}\)
BH
1
20 tháng 7 2016
Đặt tổng trên là A ta có :
A= 1/ 20 + 1/ 30 + 1/ 42 + 1/ 56 + 1/ 72 + 1/90 + 1/110 + 1 / 123 + 1/ 156
= 1 / 4 x5 + 1/ 5 x 6 + 1/6x 7 + 1/ 7x8 + 1/8x9 + 1/9x10+ 1/ 10x11+ 1 /11x12 +1/12 x 13
= 1/4- 1/5 + 1/ 5 - 1/6 + 1/ 6 - 1/7 + 1/ 7 - 1/8 + 1/8 - 1/9 + 1/9 - 1/10+ 1/10 - 1/11 + 1/11 - 1/12+ 1/ 12 - 1/13
= 1 /4 - 1 /13
= 9 /52
\(\frac{1}{10}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{90}+\frac{1}{110}\)
\(=\frac{1}{10}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{9.10}+\frac{1}{10.11}\)
\(=\frac{1}{10}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)
\(=\frac{1}{10}+\frac{1}{4}-\frac{1}{11}\)
\(=\frac{57}{220}\)
\(\frac{1}{10}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{90}+\frac{1}{110}\)
\(=\frac{1}{10}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{9.10}+\frac{1}{10.11}\)
\(=\frac{1}{10}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)
\(=\frac{1}{10}+\frac{1}{4}-\frac{1}{11}\)
\(=\frac{22}{220}+\frac{55}{220}-\frac{20}{220}\)
\(=\frac{22+55-20}{220}\)
\(=\frac{57}{220}\)