tính nhanh
\(\frac{1}{10x11}+\frac{1}{11x12}+\frac{1}{12x13}+....+\frac{1}{999x1000}\)
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NQ
1
8 tháng 6 2016
\(=7.\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+....+\frac{1}{69}-\frac{1}{70}\right)\)
\(=7.\left(\frac{1}{10}-\frac{1}{70}\right)\)
\(=7.\frac{3}{35}\)
\(=\frac{3}{5}\)
8 tháng 6 2016
= 7/10-7/11+7/11-7/12+7/12-7/13+...+7/69-7/70
=7/10-7/70
=42/70
k mk nha
NC
4
6 tháng 5 2018
a) \(F=\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+...+\frac{1}{990}\)
\(F=\frac{1}{3.6}+\frac{1}{6.9}+\frac{1}{9.12}+...+\frac{1}{30.33}\)
\(3F=\frac{3}{3.6}+\frac{3}{6.9}+\frac{3}{9.12}+...+\frac{3}{30.33}\)
\(3F=\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+...+\frac{1}{30}-\frac{1}{33}\)
\(3F=\frac{1}{3}-\frac{1}{33}\)
\(F=\frac{1}{3}.\left(\frac{1}{3}-\frac{1}{33}\right)\)
\(F=\frac{1}{3}.\frac{1}{3}-\frac{1}{3}.\frac{1}{33}=\frac{1}{9}-\frac{1}{99}=\frac{11}{99}-\frac{1}{99}=\frac{10}{99}\)
b) \(A=\frac{7}{10.11}+\frac{7}{11.12}+\frac{7}{12.13}+...+\frac{7}{69.70}\)
\(A=7.\left(\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+...+\frac{1}{69.70}\right)\)
\(A=7.\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{69}-\frac{1}{70}\right)\)
\(A=7.\left(\frac{1}{10}-\frac{1}{70}\right)=7.\left(\frac{7}{70}-\frac{1}{70}\right)=7.\frac{6}{70}\)
\(A=\frac{7.6}{70}=\frac{1.6}{10}=\frac{1.3}{5}=\frac{3}{5}\)
6 tháng 5 2018
a, \(F=\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+...+\frac{1}{990}\)
\(F=\frac{1}{3}\cdot\left(\frac{3}{3\cdot6}+\frac{3}{6\cdot9}+\frac{3}{9\cdot12}+...+\frac{3}{30\cdot33}\right)\)
\(F=\frac{1}{3}\cdot\left(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+...+\frac{1}{30}-\frac{1}{33}\right)\)
\(F=\frac{1}{3}\cdot\left(\frac{1}{3}-\frac{1}{33}\right)\)
\(F=\frac{1}{3}-\frac{10}{33}\)
\(F=\frac{10}{99}\)
DP
26 tháng 6 2017
Bài 3 :
\(A=\frac{1}{1\times2}+\frac{1}{2\times3}+....+\frac{1}{99\times100}\)
Ta có : \(\frac{1}{1\times2}=\frac{2-1}{1\times2}=\frac{2}{1\times2}-\frac{1}{1\times2}=1-\frac{1}{2}\)
\(\frac{1}{2\times3}=\frac{3-2}{2\times3}=\frac{3}{2\times3}-\frac{2}{2\times3}=\frac{1}{2}-\frac{1}{3}\)
\(\frac{1}{99\times100}=\frac{100-99}{99\times100}=\frac{100}{99\times100}-\frac{99}{99\times100}=\frac{1}{99}-\frac{1}{100}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)
\(A=1-\frac{1}{100}\)
\(A=\frac{99}{100}\)
\(B=\frac{1}{10\times11}+\frac{1}{11\times12}+...+\frac{1}{38\times39}\)
Ta có : \(\frac{1}{10\times11}=\frac{11-10}{10\times11}=\frac{11}{10\times11}-\frac{10}{10\times11}=\frac{1}{10}-\frac{1}{11}\)
\(\frac{1}{11\times12}=\frac{12-11}{11\times12}=\frac{12}{11\times12}-\frac{11}{11\times12}=\frac{1}{11}-\frac{1}{12}\)
\(\frac{1}{38\times39}=\frac{39-38}{38\times39}=\frac{39}{38\times39}-\frac{38}{38\times39}=\frac{1}{38}-\frac{1}{39}\)
\(\frac{1}{39\times40}=\frac{40-39}{39\times40}=\frac{40}{39\times40}-\frac{39}{39\times40}=\frac{1}{39}-\frac{1}{40}\)
\(\Rightarrow B=\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+....+\frac{1}{38}-\frac{1}{39}+\frac{1}{39}-\frac{1}{40}\)
\(B=\frac{1}{10}-\frac{1}{40}\)
\(B=\frac{3}{40}\)
ML
26 tháng 6 2017
3.
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
\(A=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(A=1-\frac{1}{100}\)
\(A=\frac{99}{100}\)
\(B=\frac{1}{10.11}+\frac{1}{11.12}+...+\frac{1}{38.39}+\frac{1}{39.40}\)
\(B=\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{38}-\frac{1}{39}+\frac{1}{39}-\frac{1}{40}\)
\(B=\frac{1}{10}-\frac{1}{40}\)
\(B=\frac{3}{40}\)
TP
1
HG
2 tháng 5 2020
A = 3/10x11 - 3/11x12 - .........- 3/99x100
A = 3 x ( 1/10x11 - 1/11x12 - ..... - 1/99x100 )
A = 3 x ( 11 - 10 / 10 x 11 - 12 - 11 / 11 x 12 - ...... - 100 - 99 /99 x 100 )
A = 3 x ( 11/10x11 - 10/10x11 + 12/11x12 - 11/11x12 + ......+ 100/99x100 - 99/99x100)
A = 3 x ( 1/10 - 1/11 + 1/11 - 1/12 + ......+ 1/99 - 1/100 )
A = 3 x ( 1/10 - 1/100)
A = 3 x 9/100
A = 27/100
M
1 tháng 5 2018
\(\frac{1}{11x12}+\frac{1}{12x13}+...+\frac{1}{98x99}\)= \(\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+.....+\frac{1}{98}-\frac{1}{99}\)
= \(\frac{1}{11}-\frac{1}{99}\)
= \(\frac{8}{99}\)
Học tốt !
1 tháng 5 2018
\(\frac{1}{11\times12}+\frac{1}{12\times13}+\frac{1}{13\times14}+...+\frac{1}{97\times98}+\frac{1}{98\times99}\)
\(=\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+\frac{1}{13}-\frac{1}{14}+...+\frac{1}{97}-\frac{1}{98}+\frac{1}{98}-\frac{1}{99}\)
\(=\frac{1}{11}-\frac{1}{99}\)
\(=\frac{8}{99}\)
PT
0
PT
0
HT
1
4 tháng 5 2015
C=7/10x11+7/11x12+7/12x13+.................+7/69x70
C=1x7/10x11+1x7/11x12+...........+1x7/69x70
C=7(1/10x11+1/11x12+1/12x13+....+1/69x70)
C=7(1/10-1/11+1/11-1/12+1/12-1/13+.......+1/69-1/70)
C=7(1/10-1/70)
C=7(7/70-1/70)
C=7x6/70
C=3/5
1/10×11 + 1/11×12 + 1/12×13 + ... + 1/999×1000
= 1/10 - 1/11 + 1/11 - 1/12 + 1/12 - 1/13 + ... + 1/999 - 1/1000
= 1/10 - 1/1000
= 100/1000 - 1/1000
= 99/1000
1/10×11 + 1/11×12 + 1/12×13 + ... + 1/999×1000
= 1/10 - 1/11 + 1/11 - 1/12 + 1/12 - 1/13 + ... + 1/999 - 1/1000
= 1/10 - 1/1000
= 100/1000 - 1/1000
= 99/1000