1,Tinh nhanh
1-2+3-4+5-6+7-8+9=
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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
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
A=1/1*2+1/2*3+...+1/9*10
=1-1/2+1/2-1/3+...+1/9-1/10
=(1-1/10)+(1/2-1/2)+...+(1/9-1/9)
=(10/10-1/10)+0+...+0=9/10
tổng quát: \(\frac{1}{n.\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}\)
Ta có: \(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\)
\(=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)
\(=\frac{1}{3}-\frac{1}{10}=\frac{10}{30}-\frac{3}{30}=\frac{7}{30}\)
a) 3/5x7/8:10/9=21/40:10/9=189/400
b) 3 2/7x2 1/4:1 2/5=23/7x9/4:7/5=207/28:7/5=1035/196
c) 6/9+24/15+12/9+6/15=34/15+12/9+6/15=18/5+6/15=4
d) 3 2/9-( 1 5/8+1 2/9 )=29/9-(13/8+11/9)=29/9-205/72=3/8
1-2+3-4+5-6+7-8+9 = 5
mong bạn
\(1-2+3-4+5-6+7-8+9\)
\(=9-8+7-6+5-4+3-2+1\)
\(=\left(9-8\right)+\left(7-6\right)+\left(5-4\right)+\left(3-2\right)+1\)
\(=1+1+1+1+1\)
\(=5\)