Đặt \(A'=\frac{3}{4}.\frac{5}{6}.\frac{7}{8}...\frac{4999}{5000}\)
Rõ ràng A' > A
Suy ra \(AA'>A^2=\frac{2}{50000}=\frac{1}{2500}=\left(\frac{1}{50}\right)^2\)
nên \(A< \frac{1}{50}=0,02\) đpcm
Bài 1: Tính(hợp lý nếu có thể) a) \(6\frac{5}{7}-\left(1\frac{3}{4}+2\frac{5}{7}\right)\) b) \(7\frac{5}{9}-\left(2\frac{3}{4}+3\frac{5}{9}\right)\) c) \(\frac{-3}{5}.\frac{5}{7}+\frac{-3}{5}.\frac{3}{7}+\frac{-3}{5}.\frac{6}{7}\) d) \(\frac{1}{3}.\frac{4}{5}+\frac{1}{3}.\frac{6}{5}-\frac{4}{3}\)
Bài 22, Cho \(A=\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot...\cdot\frac{99}{100}\)
\(B=\frac{2}{3}\cdot\frac{4}{5}\cdot\frac{6}{7}\cdot...\cdot\frac{100}{101}\)
1/ So sánh A và B, A2 và A.B
2/ Chứng minh A<\(\frac{1}{10}\)
Bài 21, Cho \(A=\frac{1\cdot3\cdot5\cdot...\cdot4095}{2\cdot4\cdot6\cdot...\cdot4096}\)
\(B=\frac{2\cdot4\cdot6\cdot...\cdot4096}{1\cdot3\cdot5\cdot...\cdot4097}\)
1/ So sánh A2 và A.B
2/ Chứng minh A<\(\frac{1}{64}\)
Bài 21, Cho \(A=\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot...\cdot\frac{2499}{2500}\)Chứng minh A<\(\frac{1}{49}\)
Bài 22, Cho \(A=\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot...\cdot\frac{99}{100}\)
\(B=\frac{2}{3}\cdot\frac{4}{5}\cdot\frac{6}{7}\cdot...\cdot\frac{100}{101}\)
\(C=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{4}{5}\cdot\frac{6}{7}\cdot...\cdot\frac{98}{99}\)
1/ So sánh A, B, C
2/Chứng minh \(A\cdot C< A^2< \frac{1}{10}\)
3/Chứng minh \(\frac{1}{15}< A< \frac{1}{10}\)
Bài 1: Tính (hợp lý nếu có thể)
a) \(\frac{8}{40}+\frac{-4}{20}-\frac{3}{5}\)
b) \(\frac{-7}{12}+\frac{-2}{12}-\frac{-3}{36}\)
c) \((\frac{1}{6}+\frac{-4}{13})-(\frac{-17}{6}-\frac{30}{13})\)
d) \(-\frac{-5}{4}+\frac{7}{4}-\frac{-11}{7}+\frac{2}{7}\)
e) \(-\frac{1}{8}+\frac{-7}{9}+\frac{-7}{8}+\frac{6}{7}+\frac{2}{14}\)
f) \(\frac{-2}{9}-\frac{11}{-9}+\frac{5}{7}-\frac{-6}{-7}\)
\(a,\left(9,75.21\frac{3}{7}+\frac{39}{4}.18\frac{4}{7}\right).\frac{15}{78}\)
\(b,\frac{-7}{21}+\left(1+\frac{1}{3}\right)\) \(c,\frac{2}{15}+\left(\frac{5}{9}+\frac{-6}{9}\right)\)
\(d,\left(\frac{-1}{5}+\frac{3}{12}\right)+\frac{-3}{4}\)
\(e,\frac{4}{20}+\frac{16}{42}+\frac{6}{15}+\frac{-3}{5}+\frac{2}{21}+\frac{-10}{21}+\frac{3}{20}\)
\(\frac{10+\frac{9}{2}+\frac{8}{3}+\frac{7}{4}+ \frac{6}{5}+\frac{5}{6}+\frac{4}{7}+\frac{3}{8}+\frac{2}{9}+\frac{1}{10}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{10}+\frac{1}{11}}\)
So sánh: \(A=\frac{10^5+3}{10^5-7}\) với \(B=\frac{10^5+4}{10^5-6}\)
1.tính các biểu thức sau bằng một cách hợp lí
a.\(\frac{108}{119}.\frac{107}{211}+\frac{108}{119}.\frac{104}{211}\)
b.\(\frac{15}{19}.\frac{27}{33}+\frac{15}{19}.\frac{19}{33}-\frac{15}{19}.\frac{13}{33}\)
c.\(\frac{-4}{5}.\frac{13}{10}+\frac{-4}{5}.\frac{7}{10}-\frac{-4}{5}\)
d.\(\frac{\frac{-2}{7}-\frac{-2}{15}+\frac{-2}{39}}{\frac{5}{7}-\frac{5}{15}+\frac{5}{39}}\)
e.\(\frac{3}{5}.\frac{15}{7}-\frac{15}{7}.\frac{8}{5}\)
f.\(\frac{2}{3}+\frac{1}{3}.\left(\frac{-4}{9}+\frac{5}{6}\right):\frac{7}{12}\)
h.\(\frac{\frac{3}{5}+\frac{3}{7}-\frac{3}{11}}{\frac{4}{5}+\frac{4}{7}-\frac{4}{11}}\)
g.\(\frac{3}{-4}+\frac{2}{7}+\frac{-1}{4}+\frac{5}{7}+\frac{21}{22}.\frac{66}{7}\)
k.\(\frac{27.18+27.103-120.27}{15.33+33.12}\)
l.\(\frac{\frac{2}{5}+\frac{2}{7}-\frac{2}{9}-\frac{2}{11}}{\frac{4}{5}+\frac{4}{7}-\frac{4}{9}-\frac{4}{11}}\)
giúp mik với,tý nữa mik phải nộp b rùi,giúp mik nha
\(A=\frac{5}{6}-\frac{-1}{12}+\frac{2}{3}-\frac{-2}{7}+\frac{1}{25}-\frac{-1}{4}-\frac{5}{42}\)
a,A=1-2+3+4-5-6+7+8-9-...+2007+2008-2009-2010
b, \(\frac{1}{5^2}-\frac{1}{5^3}+\frac{1}{5^4}-\frac{1}{5^5}+..-\frac{1}{5^{101}}\).CM<\(\frac{1}{30}\)
