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20 tháng 4 2017

a, Ta có : 22013 = (23)671 = 8671

31344 = (32)672 = 9672

Mà 8671 < 9672 

Vậy 22013 < 31344

b, \(A=\frac{1}{4\cdot9}+\frac{1}{9\cdot14}+\frac{1}{14\cdot19}+...+\frac{1}{64\cdot69}\)

\(A\cdot5=\frac{5}{4\cdot9}+\frac{5}{9\cdot14}+...+\frac{5}{64\cdot69}\)

\(A\cdot5=\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{64}-\frac{1}{69}\)

\(A\cdot5=\frac{1}{4}-\frac{1}{69}=\frac{65}{276}\)

\(A=\frac{65}{276}\div5=\frac{13}{276}\)

20 tháng 4 2017

a, Ta có: 22013 = (23)671 = 8671

31344 = (32)672 = 9672

Vì 8671 < 9672 => 22013 < 31344

b, A = \(\frac{1}{4.9}+\frac{1}{9.14}+\frac{1}{14.19}+...+\frac{1}{64.69}\)

5A = \(\frac{5}{4.9}+\frac{5}{9.14}+\frac{5}{14.19}+...+\frac{5}{64.69}\)

5A = \(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+\frac{1}{14}-\frac{1}{19}+...+\frac{1}{64}-\frac{1}{69}\)

5A = \(\frac{1}{4}-\frac{1}{69}=\frac{65}{276}\)

A = \(\frac{65}{276}:5=\frac{13}{276}\)

27 tháng 1 2016

13/276

27 tháng 1 2016

tich minh cho minh len thu 8 tren bang sep hang cai

29 tháng 1 2016

a 2^2015>3^1029

b 5A=\(\frac{5}{4.9}\)+\(\frac{5}{9.14}\)+\(\frac{5}{14.19}\)+.....+\(\frac{5}{64.69}\)

 5A=1/4-1/9+1/9-1/14+1/14-1/19+1/19+....+1/64-1/69

5A=1/4-1/9

A=(1/4-1/9)/5

A=1/36

29 tháng 1 2016

kho lam bo tay

\(A=\dfrac{1}{5}\left(\dfrac{5}{4\cdot9}+\dfrac{5}{9\cdot14}+...+\dfrac{5}{64\cdot69}\right)\)

\(=\dfrac{1}{5}\left(\dfrac{1}{4}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{14}+...+\dfrac{1}{64}-\dfrac{1}{69}\right)\)

\(=\dfrac{1}{5}\cdot\dfrac{65}{276}=\dfrac{13}{276}\)

20 tháng 8 2018

5B=\(\frac{5}{4\cdot9}+\frac{5}{9\cdot14}+...+\frac{5}{64\cdot69}\)

5B=\(\frac{9-4}{4\cdot9}+\frac{14-9}{9\cdot14}+...+\frac{69-64}{64.69}\)

5B=\(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{64}-\frac{1}{69}\)

5B=\(\frac{65}{276}\)

B=\(\frac{13}{276}\)

20 tháng 8 2018

\(B=\frac{1}{4.9}+\frac{1}{9.14}+....+\frac{1}{64.69}\)

\(\Rightarrow5B=\frac{5}{4.9}+\frac{5}{9.14}+...+\frac{5}{64.69}\)

\(5B=\frac{9-4}{4.9}+\frac{14-9}{9.14}+....+\frac{69-64}{64.69}\)

\(5B=\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{64}-\frac{1}{69}\)

\(5B=\frac{1}{4}-\frac{1}{69}\)

\(5B=\frac{65}{276}\)

\(B=\frac{65}{276}:5\)

\(B=\frac{13}{276}\)

b: Ta có: \(B=\dfrac{1}{4\cdot9}+\dfrac{1}{9\cdot14}+...+\dfrac{1}{64\cdot69}\)

\(=\dfrac{1}{5}\left(\dfrac{5}{4\cdot9}+\dfrac{5}{9\cdot14}+...+\dfrac{5}{64\cdot69}\right)\)

\(=\dfrac{1}{5}\left(\dfrac{1}{4}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{14}+...+\dfrac{1}{64}-\dfrac{1}{69}\right)\)

\(=\dfrac{1}{5}\cdot\dfrac{65}{4\cdot69}\)

\(=\dfrac{13}{276}\)

26 tháng 9 2021

\(A=\dfrac{2}{1\cdot4}+\dfrac{2}{4\cdot7}+...+\dfrac{2}{97\cdot100}\\ A=\dfrac{2}{3}\left(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+...+\dfrac{3}{97\cdot100}\right)\\ A=\dfrac{2}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{100}\right)\\ A=\dfrac{2}{3}\left(1-\dfrac{1}{100}\right)=\dfrac{2}{3}\cdot\dfrac{99}{100}=\dfrac{33}{50}\\ B=\dfrac{1}{4\cdot9}+\dfrac{1}{9\cdot14}+...+\dfrac{1}{64\cdot69}\\ B=\dfrac{1}{5}\left(\dfrac{5}{4\cdot9}+\dfrac{5}{9\cdot14}+...+\dfrac{5}{64\cdot69}\right)\\ B=\dfrac{1}{5}\left(\dfrac{1}{4}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{14}+...+\dfrac{1}{64}-\dfrac{1}{69}\right)\\ B=\dfrac{1}{5}\left(\dfrac{1}{4}-\dfrac{1}{69}\right)=\dfrac{1}{5}\cdot\dfrac{65}{276}=\dfrac{13}{276}\)

\(C=70\left(\dfrac{13}{56}+\dfrac{13}{72}+\dfrac{13}{90}\right)=70\cdot13\left(\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}\right)\\ C=910\left(\dfrac{1}{7\cdot8}+\dfrac{1}{8\cdot9}+\dfrac{1}{9\cdot10}\right)\\ C=910\left(\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\right)\\ C=910\left(\dfrac{1}{7}-\dfrac{1}{10}\right)=910\cdot\dfrac{3}{70}=39\)

12 tháng 1 2018

A=1/(4.9)+1/(9.14)+1/(14.19)+...+1/(64.69)

=1/5.[5/(4.9)+5/(9.14)+5/(14.19)+...+5/(64.69)]

=1/5.(1/4-1/9+1/9-1/14+1/14-1/19+...+1/64-1/69)

=1/5.(1/4-1/69)=1/5.65/276=13/276

1 tháng 2 2017

\(\frac{1}{4.9}+\frac{1}{9.14}+\frac{1}{14.19}+...+\frac{1}{44.49}\)

\(=\frac{1}{5}\left(\frac{5}{4.9}+\frac{5}{9.14}+\frac{5}{14.19}+...+\frac{5}{44.49}\right)\)

\(=\frac{1}{5}\left(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{44}-\frac{1}{49}\right)\)

\(=\frac{1}{5}\left(\frac{1}{4}-\frac{1}{49}\right)=\frac{9}{196}\)

1 tháng 2 2017

thực hiện phép tính:1-3-5-...-49/89