Tính tổng sau bằng cách nhanh nhất: 5.104 + 4.103 + 6.102 +5.10 +9
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5.104+4.103+6.102+5.10+9=10
(5+103+102+10+4+6+5)+9
=10.5125+9=51250+9=51259
\(a,2.10^3+6.10^2+0.10+1=2.1000+6.100+0+1=2601\\ b,5.10^4+7.10^3+9.10^2+1.10+5\\ =5.10000+7.1000+9.100+10+5 =57915\)
a) \(...=2000+600+0+1=2601\)
b) \(...=50000+7000+900+10+5=57915\)
a) \(23197=2\cdot10^4+3\cdot10^3+10^2+9\cdot10^1+7\)
b) \(203184=2\cdot10^5+3\cdot10^3+10^2+8\cdot10^1+4\)
a/ \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}=\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}=\)
= 1-1/8 = 7/8
b/ = (17/9+1/9)+(19/13+7/13)+(14/6+10/6) = 18/9 + 26/13 + 24/6 = 2+2+4 = 8
\(\frac{9}{10}+\frac{7}{9}+\frac{5}{8}+\frac{3}{7}+\frac{3}{5}+\frac{2}{5}+\frac{4}{7}+\frac{3}{8}+\frac{2}{9}+\frac{1}{10}\)\(\frac{1}{10}\)
= ( 9/10 + 1/10 ) + ( 7/9 + 2/9 ) + ( 5/8 + 3/8 ) + ( 3/7 + 4/7 ) + ( 3/5 + 2/5 )
= 1 + 1 + 1 + 1 + 1
= 1 x 5
= 5
\(\left(\frac{9}{10}+\frac{1}{10}\right)+\left(\frac{7}{9}+\frac{2}{9}\right)+\left(\frac{5}{8}+\frac{3}{8}\right)+\left(\frac{3}{7}+\frac{4}{7}\right)+\left(\frac{3}{5}+\frac{2}{5}\right)\)2/5)
=1+1+1+1+1=5
.
= ( 2 + 8 ) + ( 4 + 6 ) + ( 12 + 18 ) + ( 14 + 16 ) + ( 20 + 10 )
= ( 10 + 10 ) + ( 30 + 30 ) + 30
= ( 20 + 60 ) + 30
= 80 + 30
= 110
\(5.10^4+4.10^3+6.10^2+5.10+9=10\left(5+10^3+10^2+10+4+6+5\right)+9\)
\(=10.5125+9=51250+9=51259\)