tinh nhanh
-5,81.5/8+6,73:(-1,6)-1.54:(-1/3/5)
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-5,81 . 5/8 + 6,73 : (-1,6) - 1,54 : -8/5
= -5,81 . 5/8 + 6,73 : -8/5 - 1,54 : -8/5
= -5,81 .5/8 + 6,73 . -5/8 - 1,54 . -5/8
= (-5,81 - 6,73 + 1,54) . 5/8
= -11 . 5/8 = -55/8
1+1,3+1,6+.......+9,7+10
={10-1}:0,3+1=31
=1+1,3+...+10={10+1}x31:2=170,5
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0,8 x 96+1,6 x 2+1,6 x 50
=0,8 x 2 x 48+1,6 x 2+1,6 x 50
=1,6 x 48+1,6 x 2+1,5 x 50
=1,6 x (48+2+50)
=1,6 x 100
=160
1 + 9 + 2 + 8 + 3 + 7 + 4 + 6 + 5 + 5 + 6 + 4 + 7 + 3 + 8 + 2 + 9 + 1
= 10 + 10 + 10 +10 +10 + 10 + 10 + 10 + 10
= 10 x 9
= 90
tổng quát: \(\frac{1}{n.\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}\)
Ta có: \(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\)
\(=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)
\(=\frac{1}{3}-\frac{1}{10}=\frac{10}{30}-\frac{3}{30}=\frac{7}{30}\)
Đặt S = 1 x 2 + 2 x 3 + ..... + 9 x 10
3S = 1 x 2 x (3-0) + 2 x 3 x (4 - 1) + ....... + 9 x 10 x (11 - 8)
3S = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + ......... + 9 x 10 x 11 - 8 x 9 x 10
3S = ( 1 x 2 x 3 -1 x 2 x 3) + ( 2 x 3 x4 - 2 x 3 x 4) + ..... + (8 x 9 x 10 - 8 x 9 x 10) + 9 x 10 x 11
3S = 9 x 10 x 11 = 990
S = 990 : 3 = 330