Tính giá trị biểu thức:
\(A=\left[\frac{1\frac{11}{31}.4\frac{3}{7}-\left(15-6\frac{1}{3}.\frac{2}{19}\right)}{4\frac{5}{6}+\frac{1}{6}\left(12-5\frac{1}{3}\right)}.\left(-1\frac{14}{93}\right)\right].\frac{31}{50}\)
Tính
\(\frac{1\frac{11}{31}.4\frac{3}{7}-\left(15.6\frac{1}{3}.\frac{2}{19}\right)}{-4\frac{5}{6}+\frac{1}{6}.\left(12-5\frac{1}{3}\right)}.\left(-1\frac{14}{93}\right).\frac{31}{56}\)
Cho:\(A=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+.....+\frac{1}{31}\) CHỨNG MINH A BÉ HƠN 4
\(a=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+......+\frac{1}{49}-\frac{1}{50}\)\(\frac{1}{50}\) Chứng minh rằng a<\(\frac{5}{6}\)
Thực hiện phép tính:
A=\(\left(3\frac{1}{3}+2,5\right):\left(3\frac{1}{6}-4\frac{1}{5}\right)-\frac{11}{31}\)
B=\(\left(-6\right).10:\left[-0,25+\frac{1}{2}:\left(-2\right)\right]+1\frac{3}{4}\)
Tính:
M=\(\frac{1\frac{11}{31}.4\frac{3}{7}-\left(15-6\frac{1}{3}.\frac{2}{19}\right)}{4\frac{5}{8}+\frac{1}{6}.\left(12-5\frac{1}{3}\right)}\)
5like
1)\(\left[\frac{1\frac{11}{31}.4\frac{3}{7}-\left(15-6\frac{1}{3}.\frac{2}{19}\right)}{4\frac{5}{6}+\frac{1}{6}\left(12-5\frac{1}{3}\right)}.\left(-1\frac{14}{93}\right)\right].\frac{31}{50}\)
CMR :
a) \(\frac{1}{3}+\frac{1}{31}+\frac{1}{35}+\frac{1}{37}+\frac{1}{47}+\frac{1}{53}+\frac{1}{61}< \frac{1}{2}\)
b) \(\frac{1}{6}< \frac{1}{5^2}+\frac{1}{6^2}+....+\frac{1}{100^2}< \frac{1}{4}\)
Bài 1 thực hiện phép tính
a)\(\frac{45}{19}-\left(\frac{1}{2}+\left(\frac{1}{3}+\left(\frac{1}{4}\right)^{-1}\right)^{-1}\right)^{-1}.\)
b) \(\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^{10}.6^{19}-7.2^{29}.27^6}.\)
Bài 2. tìm x, biết:
a) 2(x-1) - 3(2x+2) - 4(2x+3) =16
b) \(3\frac{1}{2}:\left|2x-1\right|=\frac{21}{22}\)
c) |x2+|x-1|| = x2+2
Bài 3. Chứng minh rằng số có dạng abcabc luôn chia hết cho 11
Bài 4.tính:
a) A = \(\left(\frac{0,4-\frac{2}{9}+\frac{2}{11}}{1,4-\frac{7}{9}+\frac{7}{11}}-\frac{\frac{1}{3}-0,25+\frac{1}{5}}{1\frac{1}{6}-0,875+0,7}\right):\frac{2012}{2013}\)
b) B =\(4.\left(-\frac{1}{2}\right)^2-2.\left(-\frac{1}{2}\right)^2+3.\left(-\frac{1}{2}\right)+1\)
c) C =\(\frac{1}{2}:\left(-1\frac{1}{2}\right):1\frac{1}{3}:\left(-1\frac{1}{4}\right):1\frac{1}{5}:\left(-1\frac{1}{6}\right):...:\left(-1\frac{1}{100}\right)\)
d) D =\(\frac{4^6.9^5+6^9.120}{-8^4.3^{12}+6^{11}}\)