Question

[quan leanh]

giúp mình với

Answer 1

[Yen Nhi]

`Answer:`

\(C=\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)\left(1+\frac{1}{3.5}\right)...\left(1+\frac{1}{99.101}\right)\)

\(\Rightarrow C=\frac{1.3+1}{1.3}.\frac{2.4+1}{2.4}.\frac{3.5+1}{3.5}...\frac{99.101+1}{99.101}\)

\(\Rightarrow C=\frac{4}{1.3}.\frac{9}{2.4}.\frac{16}{3.5}...\frac{10000}{99.101}\)

\(\Rightarrow C=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}...\frac{100^2}{99.101}\)

\(\Rightarrow C=\frac{\left(2.3.4...100\right)\left(2.3.4...100\right)}{\left(1.2.3...99\right)\left(3.4.5...101\right)}\)

\(\Rightarrow C=\frac{100.2}{101}=\frac{200}{101}\)

\(D=\frac{4^7.2^8.\left(-2\right)^{-5}}{3.2^{15}.16^2-5.2^2.1024^2}\)

\(\Rightarrow D=\frac{\left(2^2\right)^7.2^8}{\left(-2\right)^5.\left(3.2^{15}.\left(2^4\right)^2-5.2^2.\left(2^{10}\right)^2\right)}\)

\(\Rightarrow D=\frac{2^{2.7+8}}{-2^5.\left(3.2^{15+2.4}-5.2^{2+2.10}\right)}\)

\(\Rightarrow D=\frac{2^{22}}{-2^5.2^{22}.\left(3.2-5\right)}\)

\(=-\frac{1}{32}\)