tính giá trị của biểu thức M=\(1+\frac{1}{2}.\left(1+2\right)+\frac{1}{3}.\left(1+2+3\right)+\frac{1}{4}.\left(1+2+3+4\right)+...+\frac{1}{16}.\left(1+2+3+...+16\right)\)
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8 tháng 8 2019
\(\left[18\frac{1}{6}-\left(0,06:7\frac{1}{2}+3\frac{2}{5}\cdot0,38\right)\right]:\left[16-2\frac{2}{3}\cdot4\frac{3}{4}\right]\)
\(< =>\left[18\frac{1}{6}-\left(\frac{1}{125}+\frac{323}{250}\right)\right]:\left[16-\frac{38}{3}\right]\)
\(< =>\left[18\frac{1}{6}-\frac{13}{10}\right]:\frac{10}{3}\)
\(< =>\frac{253}{15}:\frac{10}{3}\)
\(< =>\frac{253}{50}\)
1 tháng 12 2016
\(A=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+\frac{1}{4}\left(1+2+3+4\right)+...+\frac{1}{16}\left(1+2+3+...+16\right)\)
\(A=1+\frac{1+2}{2}+\frac{1+2+3}{3}+\frac{1+2+3+4}{4}+...+\frac{1+2+3+...+16}{16}\)
\(A=1+\frac{2\left(2+1\right):2}{2}+\frac{3\cdot\left(3+1\right):2}{3}+\frac{4\left(4+1\right):2}{4}+...+\frac{16\left(16+1\right):2}{16}\)
\(A=1+\frac{2+1}{2}+\frac{3+1}{2}+\frac{4+1}{2}+...+\frac{16+1}{2}\)
\(A=\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+\frac{5}{2}+...+\frac{17}{2}\)
\(A=\frac{2+3+4+5+...+17}{2}\)
\(A=\frac{152}{2}\)
\(A=76\)
4 tháng 5 2016
\(A=\left(3\sqrt{3}\right)^{\frac{4}{3}}+\left(\frac{1}{16}\right)^{\frac{3}{4}}+2\left(\frac{8}{27}\right)^{\frac{2}{3}}\)
\(A=\left(3\sqrt{3}\right)^{\frac{4}{3}}+55+\frac{32}{3}\)
\(A=\left(3\sqrt{3}\right)^{\frac{4}{3}}+\frac{197}{3}\)
\(A=243+\frac{197}{3}\)
\(A=\frac{926}{3}\)
4 tháng 5 2016
Ta có \(A=3^{\frac{3}{2}.\frac{4}{3}}+\left(\frac{1}{2}\right)^{4.\frac{3}{4}}+2\left(\frac{2}{3}\right)^{3.\frac{2}{3}}=3^2+\left(\frac{1}{2}\right)^3+2\left(\frac{2}{3}\right)^2=\frac{721}{72}\)
HQ
Hà Quang Minh
Giáo viên
19 tháng 9 2023
a)
\(\begin{array}{l}A = \left( {2 + \frac{1}{3} - \frac{2}{5}} \right) - \left( {7 - \frac{3}{5} - \frac{4}{3}} \right) - \left( {\frac{1}{5} + \frac{5}{3} - 4} \right).\\A = \left( {\frac{{30}}{{15}} + \frac{5}{{15}} - \frac{6}{{15}}} \right) - \left( {\frac{{105}}{{15}} - \frac{9}{{15}} - \frac{{20}}{{15}}} \right) - \left( {\frac{3}{{15}} + \frac{{25}}{{15}} - \frac{{60}}{{15}}} \right)\\A = \frac{{29}}{{15}} - \frac{{76}}{{15}} - \left( {\frac{{ - 32}}{{15}}} \right)\\A = \frac{{29}}{{15}} - \frac{{76}}{{15}} + \frac{{32}}{{15}}\\A = \frac{{ - 15}}{{15}}\\A = - 1\end{array}\)
b)
\(\begin{array}{l}A = \left( {2 + \frac{1}{3} - \frac{2}{5}} \right) - \left( {7 - \frac{3}{5} - \frac{4}{3}} \right) - \left( {\frac{1}{5} + \frac{5}{3} - 4} \right)\\A = 2 + \frac{1}{3} - \frac{2}{5} - 7 + \frac{3}{5} + \frac{4}{3} - \frac{1}{5} - \frac{5}{3} + 4\\A = \left( {2 - 7 + 4} \right) + \left( {\frac{1}{3} + \frac{4}{3} - \frac{5}{3}} \right) + \left( { - \frac{2}{5} + \frac{3}{5} - \frac{1}{5}} \right)\\A = - 1 + 0 + 0 = - 1\end{array}\)
3 tháng 12 2016
Đặt \(A=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+\frac{1}{4}\left(1+2+3+4\right)+...+\frac{1}{16}\left(1+2+3+...+16\right)\)
\(A=1+\frac{1+2}{2}+\frac{1+2+3}{3}+\frac{1+2+3+4}{4}+...+\frac{1+2+3+...+16}{16}\)
\(A=1+\frac{2\left(2+1\right):2}{2}+\frac{3\left(3+1\right):2}{3}+\frac{4\left(4+1\right):2}{4}+...+\frac{16\left(16+1\right):2}{16}\)
\(A=1+\frac{2+1}{2}+\frac{3+1}{2}+\frac{4+1}{2}+...+\frac{16+1}{2}\)
\(A=\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+\frac{5}{2}+...+\frac{17}{2}\)
\(A=\frac{2+3+4+5+...+17}{2}\)
\(A=\frac{152}{2}\)
\(A=76\)