Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(\frac{6^5.35^7}{14^7.15^5}=\frac{2^5.3^5.5^7.7^7}{2^7.7^7.3^5.5^5}=\frac{5^2}{2^2}=\frac{25}{4}\)
a)\(\frac{1}{n}-\frac{1}{n+1}=\frac{n+1}{n\left(n+1\right)}-\frac{n}{n\left(n-1\right)}=\frac{n+1-n}{n\left(n+1\right)}=\frac{1}{n\left(n+1\right)}\)
\(\Rightarrow\frac{1}{n\left(n+1\right)}=\frac{1}{n}.\frac{1}{n+1}\)
b) \(C=\frac{1}{2}.\frac{1}{3}+\frac{1}{3}.\frac{1}{4}+\frac{1}{4}.\frac{1}{5}+\frac{1}{5}.\frac{1}{6}+\frac{1}{6}.\frac{1}{7}+\frac{1}{7}.\frac{1}{8}\)
\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\)
\(=\frac{1}{2}+0+0+0+0+0-\frac{1}{8}\)
\(=\frac{1}{2}-\frac{1}{8}=\frac{4}{8}-\frac{1}{8}=\frac{4-1}{8}=\frac{3}{8}\)
a: \(=\dfrac{-4\cdot13\cdot9\cdot5}{3\cdot4\cdot5\cdot2\cdot13}=\dfrac{3}{2}\)
b: \(=\dfrac{1}{2}\cdot\dfrac{1}{3}\cdot5=\dfrac{5}{6}\)
\(\frac{2}{-5}=\frac{-24}{60}\)
\(\frac{3}{-4}=\frac{-45}{60}\)
\(\frac{6}{-24}=\frac{-1}{4}=\frac{-15}{60}\)
\(-\frac{8}{80}=\frac{-1}{10}=\frac{-6}{60}\)
\(\frac{7}{-14}=-\frac{1}{2}=\frac{-30}{60}\)
\(=\frac{\left(2.3\right)^6.\left(5.7\right)^7}{\left(2.7\right)^4.\left(3.5\right)^5}=\frac{2^6.3^6.5^7.7^7}{2^4.7^4.3^5.5^5}=\frac{2^2.3.5^2.7^3}{1.1.1.1}=\left(4.25\right).3.7^3=100.3.343=102900\)
\(\frac{2^2.3^3.5^7}{2^3.3^4.5^6}=\frac{1.1.5}{2.3.1}=\frac{5}{6}\)
Làm tương tự