\(\frac{27\cdot18+27\cdot103-27\cdot102}{15.33+33\cdot12}\)
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\(=\frac{27\left(18+103-120\right)}{33\left(15+12\right)}\)
\(=\frac{27\times1}{33\times27}\)
\(=\frac{1}{33}\)
Tính tổng: A=\(\frac{1}{1.101}+\frac{1}{2.102}+\frac{1}{3.103}+...+\frac{1}{10.110}\)
= \(\frac{1}{100}\left(\frac{1}{1}-\frac{1}{101}+\frac{1}{2}-\frac{1}{102}+...+\frac{1}{10}-\frac{1}{110}\right)\)
=\(\frac{1}{100}\left(\left(1+\frac{1}{2}+...+\frac{1}{10}\right)-\left(\frac{1}{101}+\frac{1}{102}+...+\frac{1}{110}\right)\right)\)(1)
B = \(\frac{1}{10}\left(1-\frac{1}{11}+\frac{1}{2}-\frac{1}{12}+...+\frac{1}{100}-\frac{1}{110}\right)\)
=\(\frac{1}{10}\left(1+\frac{1}{2}+..+\frac{1}{100}-\frac{1}{11}-\frac{1}{12}-...-\frac{1}{110}\right)\)
=\(\frac{1}{10}\left(\left(1+\frac{1}{2}+...+\frac{1}{10}\right)-\left(\frac{1}{101}+\frac{1}{102}+...+\frac{1}{110}\right)\right)\) (2)
Từ (1) và (2) => x = B/A = 1/10 / 1/100 = 10
\(\frac{27.18+27.103-27.102}{15.33+33.12}=\frac{27\left(18+103-102\right)}{33\left(15+12\right)}\)
\(=\frac{27.19}{33.27}=\frac{19}{33}\)
k nha
\(\frac{27.18+27.103-27.102}{15.33+33.12}=\frac{27.\left(18+103-102\right)}{33.\left(15+12\right)}=\frac{27.19}{33.27}=\frac{19}{33}\)