=1.1.3.3.5.5...99.99/1.3.3.5.5.7.....99.101
=(1.3.5..99/1.3.5....99).(1.3.5....99/3.5.7...101)
=1.1/101
=1/101
=1.1.3.3.5.5...99.99/1.3.3.5.5.7.....99.101
=(1.3.5..99/1.3.5....99).(1.3.5....99/3.5.7...101)
=1.1/101
=1/101
=1.1.3.3.5.5...99.99/1.3.3.5.5.7.....99.101
=(1.3.5..99/1.3.5....99).(1.3.5....99/3.5.7...101)
=1.1/101
=1/101
=1.1.3.3.5.5...99.99/1.3.3.5.5.7.....99.101
=(1.3.5..99/1.3.5....99).(1.3.5....99/3.5.7...101)
=1.1/101
=1/101
Rút gọn:
\(A=\frac{1}{1-\sqrt{2}}-\frac{1}{\sqrt{2}-\sqrt{3}}+\frac{1}{\sqrt{3}-\sqrt{4}}+...+\frac{1}{\sqrt{99}-\sqrt{100}}\)
rút gọn \(C=\frac{1^2}{2^2-1}\cdot\frac{3^2}{4^2-1}\cdot\frac{5^2}{6^2-1}...\frac{n^2}{\left(n+1\right)^2-1}\)
Rút gọn:
B= \(\frac{1^2}{2^2-1}.\frac{3^2}{4^2-1}.\frac{5^2}{6^2-1}....\frac{\left(2n+1\right)^2}{\left(2n+2\right)^2-1}\)
1-a,\(A=\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+...+\frac{1}{\sqrt{n-1}+\sqrt{n}}\)
b,\(B=\frac{1}{2+\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\frac{1}{4\sqrt{3}+3\sqrt{4}}+...+\frac{1}{100\sqrt{99}+99\sqrt{100}}\)
Rút gọn biểu thức: M=\(\frac{1}{x^2+3x+2}+\frac{1}{x^2+5x+6}+\frac{1}{x^2+7x+12}+\frac{1}{x^2+9x+20}+\frac{1}{x+5}\)
\(\frac{\frac{x+1}{\left(x+1\right)^2-x}-\frac{2}{x+2}}{\frac{\left(x+1\right)^4+2}{\left(x+1\right)^3+1}-x-1}\)với x=100 hãy rút gọn rồi tính giá trị biểu thức
1/ Rút gọn : \(\frac{5^2-1}{3^2-1}:\frac{9^2-1}{7^2-1}:\frac{13^2-1}{11^2-1}:......:\frac{55^2-1}{53^2-1}\)
\(P=\frac{x+2}{x+3}-\frac{5}{x^2+x-6}+\frac{1}{2-x}\)
1. Tìm ĐKXĐ và Rút gọn
2. Tìm x để P= 3/4
Rút gọn:
\(\frac{1}{\left(x+y\right)^3}\cdot\left(\frac{1}{x^3}+\frac{1}{y^3}\right)+\frac{3}{\left(x+y\right)^4}\cdot\left(\frac{1}{x^2}+\frac{1}{y^2}\right)+\frac{6}{\left(x+y\right)^5}\cdot\left(\frac{1}{x}+\frac{1}{y}\right)\)