Question

Tính :

-3 + \(\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{3}}}}\)

giúp mình với

Answer 1

\(-3+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{3}}}}\)

\(=-3+\frac{1}{1+\frac{1}{1+\frac{1}{\frac{4}{3}}}}\)

\(=-3+\frac{1}{1+\frac{1}{1+\frac{3}{4}}}\)
\(=-3+\frac{1}{1+\frac{1}{\frac{7}{4}}}\)

\(=-3+\frac{1}{1+\frac{4}{7}}\)

\(=-3+\frac{1}{\frac{11}{7}}\)

\(=-3+\frac{7}{11}\)

\(=-\frac{26}{11}\)

Answer 2

Ta có: \(A=-3+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{3}}}}=-3+\frac{1}{1+\frac{1}{1+\frac{1}{\left(\frac{4}{3}\right)}}}\)

\(=-3+\frac{1}{1+\frac{1}{\frac{4}{4}+\frac{3}{4}}}=-3+\frac{1}{1+\frac{1}{\left(\frac{7}{4}\right)}}\)

\(=-3+\frac{1}{\frac{7}{7}+\frac{4}{7}}=-3+\frac{1}{\left(\frac{11}{7}\right)}=-3+\frac{7}{11}=-\frac{26}{11}\)

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