4.Tính giá trị biểu thức sau bắng cách thuận tiện
\(\dfrac{1}{1x2}\)+\(\dfrac{2}{2x4}\)+\(\dfrac{3}{4x7}\)+\(\dfrac{4}{7x11}\)+...+\(\dfrac{8}{29x37}\)+\(\dfrac{9}{37x46}\)+\(\dfrac{10}{46x56}\)
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NB
2 tháng 3 2023
1/1x2 + 2/2x4 + 3/4x7 + 4/7x11 +...+ 8/29x37 + 9/37x46
=2-1/1x2+4-2/2x4+...+46-37/37x46
=1-1/2+1/2-1/4+...+1/37-1/46
=1-1/46
=45/46
16 tháng 4 2022
\(\dfrac{1}{10}+\dfrac{2}{10}+\dfrac{3}{10}+\dfrac{4}{10}+\dfrac{5}{10}+\dfrac{6}{10}+\dfrac{7}{10}+\dfrac{8}{10}+\dfrac{9}{10}\)
\(=\left(\dfrac{1}{10}+\dfrac{9}{10}\right)+\left(\dfrac{2}{10}+\dfrac{8}{10}\right)+\left(\dfrac{3}{10}+\dfrac{7}{10}\right)+\left(\dfrac{4}{10}+\dfrac{6}{10}\right)+\dfrac{5}{10}\)
\(=1+1+1+1+\dfrac{5}{10}\)
\(=4+\dfrac{5}{10}\)
\(=\dfrac{45}{10}\)
\(13,25:0,5+13,25:0,25+13,25:0,125+13,25\times6\)
\(=13,25:\dfrac{1}{2}+13,25:\dfrac{1}{4}+13,25:\dfrac{1}{8}+13,25\times6\)
\(=13,25\times2+13,25\times4+13,25\times8+13,25\times6\)
\(=13,25\times\left(2+4+8+6\right)\)
\(=13,25\times20\)
\(=265\)
12 tháng 11 2022
60x [7/12+4/15]
60x153/180
=9180/180
b 1/2x2/3x3/4x4/5x5/6x6/7x7/8x8/9=40320/4032
DC
17 tháng 3 2022
\(\dfrac{6}{7}+\dfrac{5}{8}:5-\dfrac{3}{16}.\left(-2\right)^2=\dfrac{6}{7}+\dfrac{5}{8}:5-\dfrac{3}{16}.4=\dfrac{6}{7}+\dfrac{1}{8}-\dfrac{3}{4}=\dfrac{5}{56}\)
\(\dfrac{2}{3}+\dfrac{1}{3}.\left(-\dfrac{4}{9}+\dfrac{5}{6}\right):\dfrac{7}{12}=\dfrac{2}{3}+\dfrac{1}{3}.\dfrac{7}{18}:\dfrac{7}{12}=\dfrac{2}{3}+\dfrac{2}{9}=\dfrac{8}{9}\)
HQ
Hà Quang Minh
Giáo viên
5 tháng 10 2023
\(B=\frac{1}{3}.b+\frac{2}{9}.b– b: \frac{9}{4}= \frac{1}{3}.b+\frac{2}{9}.b – b. \frac{4}{9}\)
\(=b(\frac{1}{3}+\frac{2}{9}-\frac{4}{9})=b. (\frac{3}{9}+\frac{2}{9}-\frac{4}{9})= b. \frac{1}{9} \)
Thay \(b=\frac{9}{10}\) vào B, ta được
B= \(b=\frac{9}{10}. \frac{1}{9}= \frac{1}{10}\)
A = \(\dfrac{1}{1\times2}\)+\(\dfrac{2}{2\times4}\)+\(\dfrac{3}{4\times7}\)+...+\(\dfrac{9}{37\times46}\)+\(\dfrac{10}{46\times56}\)
A = \(\dfrac{1}{1}\) - \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{4}\)+ \(\dfrac{1}{4}\) - \(\dfrac{1}{7}\) + ... + \(\dfrac{1}{37}\) - \(\dfrac{1}{46}\) + \(\dfrac{1}{46}\) - \(\dfrac{1}{56}\)
A = \(\dfrac{1}{1}\) - \(\dfrac{1}{56}\)
A = \(\dfrac{55}{56}\)