\(B=\frac{2,5-4.\left(\frac{5}{2}-1,2\right)+\frac{3}{8}}{4.\left(\frac{5}{2}-1,2\right)-\frac{3}{5}:\frac{2}{5}}-\frac{55}{148}\)

\(B=\frac{\frac{5}{2}-4.\left(\frac{25}{10}-\frac{12}{10}\right)+\frac{3}{8}}{4.\left(\frac{25}{10}-\frac{12}{10}\right)-\frac{3}{5}.\frac{5}{2}}-\frac{55}{148}\)

\(B=\frac{\frac{5}{2}-4.\frac{13}{10}+\frac{3}{8}}{4.\frac{13}{10}-\frac{3}{2}}-\frac{55}{148}\)

\(B=\frac{\frac{5}{2}-\frac{26}{5}+\frac{3}{8}}{\frac{26}{5}-\frac{3}{2}}-\frac{55}{148}\)

\(B=\frac{\frac{100}{40}-\frac{208}{40}+\frac{15}{40}}{\frac{52}{10}-\frac{15}{10}}-\frac{55}{148}\)

\(B=\frac{-\frac{93}{40}}{\frac{37}{10}}-\frac{55}{148}\)

\(B=\frac{93}{148}-\frac{55}{148}\)

\(B=\frac{19}{74}\)

=5*[55+13+32]

=5*100                     [* là dấu nhân]

=500

5x55+13x5+32

=5x(55+13+32)

=5x100

=500

đơn giản 

nhưng trả lời câu hỏi của tớ đã

\(5+5^3+5^5+5^7+..+5^{27}\)

\(=\left(5+5^3\right)+5^4\left(5+5^3\right)+...+5^{24}\left(5+5^3\right)\)

\(=130+130\cdot5^4+...+130\cdot5^{24}\)

\(=130\left(1+5^4+..5^{24}\right)\)

Vì \(130⋮26\Rightarrow5+5^3+5^5+...+5^{27}⋮26\left(đpcm\right)\)

109

198

\(\frac{7}{18}+\frac{5}{3}\times1\frac{3}{9}\div\frac{55}{4}=\)\(\frac{7}{18}+\frac{5}{3}\times\frac{12}{9}\div\frac{55}{4}=\)\(\frac{7}{18}+\frac{5}{3}\times\frac{12}{9}\times\frac{4}{55}=\)\(\frac{7}{18}+\frac{5\times12\times4}{3\times9\times55}=\)\(\frac{7}{18}+\frac{4\times4}{9\times11}=\)\(\frac{7}{18}+\frac{16}{99}=\)\(\frac{693}{1782}+\frac{288}{1782}=\)\(\frac{981}{1782}=\frac{109}{198}\)

Ta có: \(1\times10+2\times9+\cdots+10\times1\)

\(=2\times\left(1\times10+2\times9+\cdots+5\times6\right)\)

\(=2\times\left(11+18+24+28+30\right)=2\times111=222\)

\(1+3+6+\cdots+45+55\)

\(=\frac{1\times2}{2}+\frac{2\times3}{2}+\frac{3\times4}{2}+\cdots+\frac{9\times10}{2}+\frac{10\times11}{2}\)

\(=\frac12\times\left(1\times2+2\times3+\cdots+10\times11\right)\)

\(=\frac12\times\left\lbrack1\times\left(1+1\right)+2\times\left(2+1\right)+\cdots+10\times\left(10+1\right)\right\rbrack\)

\(=\frac12\times\left\lbrack\left(1\times1+2\times2+\cdots+10\times10\right)+\left(1+2+\cdots+10\right)\right\rbrack\)

\(=\frac12\times\left\lbrack\frac{10\times\left(10+1\right)\times\left(2\times10+1\right)}{6}+\frac{10\times11}{2}\right\rbrack\)

\(=\frac12\times\left\lbrack\frac{10\times11\times21}{6}+5\times11\right\rbrack=\frac12\times\left\lbrack5\times11\times7+5\times11\right\rbrack\)

\(=\frac12\times55\times\left(7+1\right)=55\times\frac82=55\times4=220\)

Ta có: \(\frac{1+3+6+\cdots+45+55}{1\times10+2\times9+\cdots+10\times1}\)

\(=\frac{220}{222}=\frac{110}{111}\)