THU GỌN BIỂU THỨC SAU
\(\frac{2^3-1}{2^3+1}.\frac{3^3-1}{3^3+1}.\frac{4^3-1}{4^3+1}...\frac{n^3-1}{n^3+1}\)
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THU GỌN BIỂU THỨC SAU
\(\frac{2^3-1}{2^3+1}.\frac{3^3-1}{3^3+1}.\frac{4^3-1}{4^3+1}...\frac{n^3-1}{n^3+1}\)
THU GỌN BIỂU THỨC SAU
\(\left(\frac{n-1}{1}+\frac{n-2}{2}+\frac{n-3}{3}+...+\frac{2}{n-2}+\frac{1}{n-1}\right):\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{n}\right)\)
THU GỌN BIỂU THỨC SAU
\(\left(\frac{n-1}{1}+\frac{n-2}{2}+\frac{n-3}{3}+...+\frac{2}{n-2}+\frac{1}{n-1}\right):\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{n}\right)\)
rút gọn cấc phân thức sau:
\(A=\frac{2^3-1}{2^3+1}\frac{3^3-1}{3^3+1}\frac{4^3-1}{4^3+1}\cdot\cdot\cdot\frac{n^3-1}{n^3+1}\)
\(\frac{n^3-1}{n^3+1}=\frac{\left(n-1\right)\left(n^2+n+1\right)}{\left(n+1\right)\left(n^2-n+1\right)}=\frac{\left(n-1\right)\left[\left(n+1\right)^2-\left(n+1\right)+1\right]}{\left(n+1\right)\left(n^2-n+1\right)}\)
\(\Rightarrow A=\frac{1\left(3^2-3+1\right)}{3\left(2^2-2+1\right)}.\frac{2.\left(4^2-4+1\right)}{4.\left(3^2-3+1\right)}.\frac{3\left(5^2-5+1\right)}{5.\left(4^2-4+1\right)}...\frac{\left(n-1\right)\left[\left(n+1\right)^2-\left(n+1\right)+1\right]}{\left(n+1\right)\left(n^2-n+1\right)}\)
\(=\frac{1.2.\left[\left(n+1\right)^2-\left(n+1\right)+1\right]}{\left(2^2-2+1\right).n\left(n+1\right)}=\frac{2\left(n^2+n+1\right)}{3\left(n^2+n\right)}\)
Rút gọn phân thức sau : \(\frac{2^3-1}{2^3+1}.\frac{3^3-1}{3^3+1}.\frac{4^3-1}{4^3+1}......\frac{n^3-1}{n^3+1}\) (với n\(\in\) N, n>3)
Rút gọn biểu thức:
\(B=\left(\frac{n-1}{1}+\frac{n-2}{2}+\frac{n-3}{3}+...+\frac{2}{n-2}+\frac{1}{n-1}\right):\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{n}\right)\) + \(\frac{1}{n}\) )
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THU GỌN BIỂU THỨC :
\(M=\frac{1}{^7}+\frac{1}{7^3}+\frac{1}{7^5}+...+\frac{1}{7^{2011}}\)
\(N=\frac{1}{4}-\frac{1}{4^2}+\frac{1}{4^3}-\frac{1}{4^4}+...+\frac{1}{4^{99}}-\frac{1}{4^{100}}\)
Thu gọn biểu thức sau:
\(N=\frac{1}{2}-\frac{1}{^{2^2}}+\frac{1}{2^3}-\frac{1}{2^4}+...+\frac{1}{2^{49}}-\frac{1}{2^{50}}\)
rút gọn biểu thức B=\(\frac{1}{\sqrt[3]{1}+\sqrt[3]{2}+\sqrt[3]{4}}\)+\(\frac{1}{\sqrt[3]{4}+\sqrt[3]{6}+\sqrt[3]{9}}\)+....+\(\frac{1}{\sqrt[3]{n^2}+\sqrt[3]{n\left(n+1\right)}+\sqrt[3]{\left(n+1\right)^2}}\)