Các câu hỏi tương tự
tính GTBT:
N=\(\frac{-1^2}{1\cdot2}\cdot\frac{-2^2}{2\cdot3}\cdot\frac{-3^2}{3\cdot4}\cdot\cdot\cdot\frac{-100^2}{100\cdot101}\cdot\frac{-101^2}{101\cdot102}\)
Tính \(A=\frac{\left(1+2+3+...+100\right)\cdot\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{4}-\frac{1}{5}\right)\cdot\left(2,4\cdot42-21\cdot4,8\right)}{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}}\)
Chứng minh rằng:
\(A=\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot\frac{7}{8}\cdot...\cdot\frac{99}{100}
Chứng minh \(A=\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot\frac{7}{8}\cdot...\cdot\frac{99}{100}<\frac{1}{\sqrt{151}}\)
Chứng minh rằng:
\(A=\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot\frac{7}{8}\cdot...\cdot\frac{99}{100}<\frac{1}{\sqrt{151}}\)
Tính
a)\(5^2-\left(-5\right)^3+\frac{1}{2}-\left(\frac{1}{2}\right)^2\)
b)\(2\frac{3}{4}-\frac{1}{8}\cdot1\frac{1}{2}\)
c)\(\left(\frac{1}{3^5}+\frac{1}{3^6}+\frac{1}{3^7}+\frac{1}{3^8}\right)\cdot3^9\)
d)\(\left(\frac{1}{2^2}-1\right)\cdot\left(\frac{1}{3^2}-1\right)\cdot\cdot\cdot\cdot\left(\frac{1}{100^2}-1\right)\)
\frac{2}{2\cdot 4}+\frac{2}{4\cdot 6}+\frac{2}{6\cdot 8}+...+\frac{2}{98\cdot 100}
Cho B=\(\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot...\cdot\frac{99}{100}.\)CMR\(\frac{1}{15}< B< \frac{1}{10}\)
Tính giá trị các biểu thức:
a)\(A=\frac{12}{3\cdot7}+\frac{12}{7\cdot11}+...+\frac{12}{195\cdot199}\)
b)\(B=\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot...\cdot\frac{2499}{2500}\)
c)\(C=\frac{1}{2}-\frac{1}{2^2}+\frac{1}{2^3}-\frac{1}{2^4}+...+\frac{1}{2^{99}}-\frac{1}{2^{100}}\)