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A=1/2+1/6+1/12+1/20+...+1/72+1/90
A=1/1x2+1/2x3+1/3x4+1/4x5+.....+1/8x9+1/9x10
A=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+....+1/8-1/9+1/9-1/10
A=1-1/10
A=9/10
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T
4 tháng 12 2016
Ta có:\(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+..+\frac{2}{210}=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+..+\frac{2}{14.15}\) \(=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+..+\frac{1}{14}-\frac{1}{15}\right)\) \(=2.\left(\frac{1}{2}-\frac{1}{15}\right)\) \(=1-\frac{2}{15}=\frac{15-2}{15}=\frac{13}{15}\) 4 tháng 12 2016
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NT
1
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
18 tháng 7 2023
A = \(\dfrac{1}{2}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{12}\) + \(\dfrac{1}{20}\) + \(\dfrac{1}{30}\)+...+\(\dfrac{1}{182}\)+ 210 A = \(\dfrac{1}{1\times2}\) + \(\dfrac{1}{2\times3}\)+\(\dfrac{1}{3\times4}\)+ \(\dfrac{1}{4\times5}\)+...+ \(\dfrac{1}{13\times14}\)+ 210 A = \(\dfrac{1}{1}\) - \(\dfrac{1}{2}\)+ \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\)+ \(\dfrac{1}{3}\)- \(\dfrac{1}{4}\)+ \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\)+...+\(\dfrac{1}{13}\) - \(\dfrac{1}{14}\) + 210 A = 1 - \(\dfrac{1}{14}\) + 210 A = 211 - \(\dfrac{1}{14}\) A = \(\dfrac{2953}{14}\)
TP
6 tháng 8 2017
Ta có: A = 1 + 3 + 5 + 7 +... + 101 A = \(\frac{102.51}{2}=2601\) M = 16 - 18 + 20 - 22 + 24 - 26 + .. + 64 - 66 + 68 M = ( 16 - 18 ) + ( 20 - 22 ) + ( 24 - 26 ) + ... + ( 64 - 66 ) + 68 M = (- 2 + - 2 + -2 + ... + - 2 ) + 68 M = 25/2 . ( - 2 ) + 68 M = -25 + 68 M = 43 H = ( 1 + 2 + 3 +...+ 99 ) x ( 13 x 15 - 12 x 15 - 15 ) H = ( 1 + 2 + 3 +...+ 99 ) x { (13 - 12 - 1) x 15 } H = ( 1 + 2 + 3 +...+ 99 ) x 0 H = 0 G = 1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + 9 + 10 - 11 - 12 + 13 + 14 - ... + 301 + 302 G = ( 1 + 2 ) + ( -3 - 4 ) + ( 5 + 6 ) + ( -7 - 8 ) + ( 9 + 10 ) + ( - 11 - 12 ) + ( 13 + 14 ) -...+ ( 301 + 302 ) G = ( 3 - 7 ) + ( 11 - 15 ) + ( 19 - 23 ) + 27 - ... + 603 G = -4 + - 4 + -4 + 27 - ... + 603 G = 75 x ( -4 ) + 603 G = -300 + 603 G = 303 2. a) 1 + 2 + 3 + 4 +...+ 99 + 100 + 2 x X = 5052 = > \(\frac{100.101}{2}\)+ 2 x X = 5052 = > 5050 + 2 x X = 5052 = > 2X = 2 = > X = 1 26 tháng 8 2016
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}\) \(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}\) \(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}\) \(=1-\frac{1}{5}\) \(=\frac{4}{5}\) \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{9900}\) \(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{98.99}+\frac{1}{99.100}\) \(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}+\frac{1}{100}\) \(=1-\frac{1}{100}\) \(=\frac{99}{100}\) |