Cho \(A=\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.\frac{7}{8}.....\frac{79}{80}.CMR\)
\(A<\frac{1}{9}\)
Bài 1 : Tính
Cho A =\(\frac{1}{31}+\frac{1}{32}+\frac{1}{33}+......+\frac{1}{60}>\frac{7}{12}\)
B = \(\frac{1}{3^2}+\frac{1}{3^2}+\frac{1}{5^2}+......+\frac{ }{50^{21}}\)
CMR B >\(\frac{1}{4}\)và B < \(\frac{4}{9}\)
C = \(\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.\frac{7}{8}.......\frac{79}{80}< \frac{1}{9}\)
Bài 1 : Cho A = \(\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.\frac{7}{8}...\frac{79}{80}\)
Chứng minh rằng A < \(\frac{1}{9}\)
Bài 4 : Chứng minh rằng: 1.3.5.7....19 = \(\frac{11}{2}.\frac{12}{2}.\frac{13}{2}...\frac{20}{2}\)
\(\frac{1}{2}-\frac{2}{3}+\frac{3}{4}-\frac{4}{5}-\left(\frac{-5}{6}\right)-\frac{6}{7}-\frac{-7}{8}+\frac{6}{7}-\frac{5}{6}+\frac{4}{5}-\frac{3}{4}+\frac{2}{3}-\frac{1}{2}\)
Tính hợp lý
\(\frac{\frac{5}{3}+\frac{5}{8}-\frac{5}{7}}{\frac{-4}{3}-\frac{-4}{8}+\frac{4}{7}}:\frac{\frac{2}{3}-\frac{1}{6}+\frac{6}{7}}{\frac{-1}{3}+\frac{1}{6}-\frac{1}{7}}\)
Cho \(A=\frac{1}{2}.\frac{3}{4}.\frac{5}{6}...\frac{79}{80}\)và \(\frac{1}{9}\). Hãy so sánh
\(A=\left(1\frac{1}{6}\times\frac{6}{7}\times6:\frac{3}{5}\right):\left(4\frac{1}{5}\times\frac{10}{11}+5\frac{2}{10}\right)\)
\(B=1\frac{13}{15}\times25\%\times3+\left(\frac{8}{15}-\frac{79}{60}\right):1\frac{23}{4}\)
\(C=\frac{123}{4567}\times\frac{1}{8}+\frac{123}{4567}\times\frac{1}{2}-\frac{123}{4567}\times\frac{13}{8}\)
\(D=\frac{10\frac{1}{3}\times\left(24\frac{1}{2}-15\frac{6}{7}\right)-\frac{12}{11}\times\left(\frac{10}{3}-1,75\right)}{\left(\frac{5}{9}-0,25\right)\times\frac{60}{11}+194\frac{8}{99}}\)
Tính nhanh: \(\frac{3}{1!+2!+3!}+\frac{4}{2!+3!+4!}+\frac{5}{3!+4!+5!}+\frac{6}{4!+5!+6!}+\frac{7}{5!+6!+7!}+\frac{8}{6!+7!+8!}\)
