Question

Tính

 \(_{\frac{2^{76}-2^{74}}{2^{78}-2^{76}}}\)

b)\(\left(1+\frac{1}{11}\right)\left(1+\frac{1}{12}\right).....\left(1+\frac{1}{16}\right)\)

Answer 1

\(\frac{2^{76}-2^{74}}{2^{78}-2^{76}}=\frac{2^{74}\left(2^2-1\right)}{2^{74}\left(2^4-2^2\right)}=\frac{4-1}{16-4}=\frac{1}{4}\)

\(1+\frac{1}{11}=\frac{12}{11}\)

\(1+\frac{1}{12}=\frac{13}{12}\)

\(1+\frac{1}{13}=\frac{14}{13}\)

\(1+\frac{1}{14}=\frac{15}{14}\)

\(1+\frac{1}{15}=\frac{16}{15}\)

\(1+\frac{1}{16}=\frac{17}{16}\)

\(\left(1+\frac{1}{11}\right)\left(1+\frac{1}{12}\right)...\left(1+\frac{1}{16}\right)=\frac{12.13.14.15.16.17}{11.12.13.14.15.16}=\frac{17}{11}\)