a) So sánh:
22013 và 31344
b) Tính:
A=1/4.9+1/9.14+1/14.19+......+1/64.69
K
Khách
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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
14 tháng 6 2022
\(A=\dfrac{1}{5}\left(\dfrac{5}{4\cdot9}+\dfrac{5}{9\cdot14}+...+\dfrac{5}{64\cdot69}\right)\)
\(=\dfrac{1}{5}\left(\dfrac{1}{4}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{14}+...+\dfrac{1}{64}-\dfrac{1}{69}\right)\)
\(=\dfrac{1}{5}\cdot\dfrac{65}{276}=\dfrac{13}{276}\)
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=\(\frac{13}{276}\)
KD
20 tháng 8 2018
\(B=\frac{1}{4.9}+\frac{1}{9.14}+....+\frac{1}{64.69}\)
\(\Rightarrow5B=\frac{5}{4.9}+\frac{5}{9.14}+...+\frac{5}{64.69}\)
\(5B=\frac{9-4}{4.9}+\frac{14-9}{9.14}+....+\frac{69-64}{64.69}\)
\(5B=\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{64}-\frac{1}{69}\)
\(5B=\frac{1}{4}-\frac{1}{69}\)
\(5B=\frac{65}{276}\)
\(B=\frac{65}{276}:5\)
\(B=\frac{13}{276}\)
26 tháng 9 2021
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
\(A=\dfrac{2}{1\cdot4}+\dfrac{2}{4\cdot7}+...+\dfrac{2}{97\cdot100}\\ A=\dfrac{2}{3}\left(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+...+\dfrac{3}{97\cdot100}\right)\\ A=\dfrac{2}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{100}\right)\\ A=\dfrac{2}{3}\left(1-\dfrac{1}{100}\right)=\dfrac{2}{3}\cdot\dfrac{99}{100}=\dfrac{33}{50}\\ B=\dfrac{1}{4\cdot9}+\dfrac{1}{9\cdot14}+...+\dfrac{1}{64\cdot69}\\ B=\dfrac{1}{5}\left(\dfrac{5}{4\cdot9}+\dfrac{5}{9\cdot14}+...+\dfrac{5}{64\cdot69}\right)\\ B=\dfrac{1}{5}\left(\dfrac{1}{4}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{14}+...+\dfrac{1}{64}-\dfrac{1}{69}\right)\\ B=\dfrac{1}{5}\left(\dfrac{1}{4}-\dfrac{1}{69}\right)=\dfrac{1}{5}\cdot\dfrac{65}{276}=\dfrac{13}{276}\)
\(C=70\left(\dfrac{13}{56}+\dfrac{13}{72}+\dfrac{13}{90}\right)=70\cdot13\left(\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}\right)\\ C=910\left(\dfrac{1}{7\cdot8}+\dfrac{1}{8\cdot9}+\dfrac{1}{9\cdot10}\right)\\ C=910\left(\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\right)\\ C=910\left(\dfrac{1}{7}-\dfrac{1}{10}\right)=910\cdot\dfrac{3}{70}=39\)
TY
2
1 tháng 2 2017
\(\frac{1}{4.9}+\frac{1}{9.14}+\frac{1}{14.19}+...+\frac{1}{44.49}\)
\(=\frac{1}{5}\left(\frac{5}{4.9}+\frac{5}{9.14}+\frac{5}{14.19}+...+\frac{5}{44.49}\right)\)
\(=\frac{1}{5}\left(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{44}-\frac{1}{49}\right)\)
\(=\frac{1}{5}\left(\frac{1}{4}-\frac{1}{49}\right)=\frac{9}{196}\)
RN
0
RN
0
a, Ta có : 22013 = (23)671 = 8671
31344 = (32)672 = 9672
Mà 8671 < 9672
Vậy 22013 < 31344
b, \(A=\frac{1}{4\cdot9}+\frac{1}{9\cdot14}+\frac{1}{14\cdot19}+...+\frac{1}{64\cdot69}\)
\(A\cdot5=\frac{5}{4\cdot9}+\frac{5}{9\cdot14}+...+\frac{5}{64\cdot69}\)
\(A\cdot5=\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{64}-\frac{1}{69}\)
\(A\cdot5=\frac{1}{4}-\frac{1}{69}=\frac{65}{276}\)
\(A=\frac{65}{276}\div5=\frac{13}{276}\)
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 = \(\frac{65}{276}:5=\frac{13}{276}\)