B=\(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{2012}}\)
=>3B=\(1+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{2011}}\)
=>3B-B=2B=1-\(\dfrac{1}{3^{2012}}\)
=>B=\(\dfrac{1}{2}-\dfrac{1}{2.3^{20112}}\)<1/2
vậy........
Câu 1: Tinh
\(A=\left(\dfrac{3}{5}\right)^2.5^2-\left(2\dfrac{1}{4}\right)^3:\left(\dfrac{3}{4}\right)^3+\dfrac{1}{2}\)
\(B=\left[\dfrac{4}{11}.\left(\dfrac{1}{25}\right)^0+\dfrac{7}{22}.2\right]^{2010}-\left(\dfrac{1}{2^2}:\dfrac{8^2}{4^4}\right)^{2009}\)
\(\dfrac{7}{8}.\left(\dfrac{2}{12}+\dfrac{4}{10}\right)\)
\(\dfrac{3}{2}-\dfrac{5}{6}:\left(\dfrac{1}{2}\right)^2+\sqrt{4}\)
Câu 2: Tim x
\(2.x-\dfrac{5}{4}=\dfrac{20}{15}\)
\(\left(x+\dfrac{1}{3}\right)^3=\left(\dfrac{-1}{8}\right)\)
Tính hợp lí
a)\(\dfrac{2-\dfrac{1}{3}+\dfrac{1}{4}}{2+\dfrac{1}{6}-\dfrac{1}{4}}+\dfrac{\dfrac{3}{5}-\dfrac{1}{4}+\dfrac{5}{10}}{\dfrac{1}{2}+\dfrac{3}{4}-\dfrac{2}{5}}\)
b)\(\dfrac{\dfrac{5}{79}+\dfrac{5}{83}+\dfrac{1}{17}}{\dfrac{17}{79}+\dfrac{17}{83}+\dfrac{1}{5}}\)
Tìm X, biết
a, X+ \(\dfrac{5}{6}=\dfrac{2}{5}-\dfrac{-2}{3}\)x
b,\(1\dfrac{2}{5}x+\dfrac{3}{7}=\dfrac{-4}{5}-\dfrac{1}{5}x\)
c,\(\dfrac{1}{3}-\dfrac{2}{3}\left(x-\dfrac{1}{2}\right)=1\)
Tìm x biết:
a) \(\left|x-\dfrac{1}{2}\right|+\left|x+2\right|=\dfrac{3}{4}\)
b) \(\left(\dfrac{2}{3}-2x\right).1\dfrac{1}{2}=\dfrac{3}{4}\)
c) \(\left|x-1\right|+2\left(x+4\right)=10\)
d) \(\dfrac{11}{12}+\dfrac{11}{12.23}+...+\dfrac{11}{89.100}+x=1\dfrac{2}{3}\)
e) \(\left(\dfrac{2}{11.13}+\dfrac{2}{13.15}+...+\dfrac{2}{19.21}\right)-x+4\dfrac{221}{231}=2\dfrac{1}{3}\)
Cho biểu thức \(A=\dfrac{1}{3}+\left(\dfrac{1}{3}\right)^2+\left(\dfrac{1}{3}\right)^3+...+\left(\dfrac{1}{3}\right)^{2019}+\left(\dfrac{1}{3}\right)^{2020}\). Chứng minh rằng A \(< \dfrac{1}{2}\)
Giúp mk đi, 23h là mk phải nộp rùi
Tìm x , biết :
1, |\(\dfrac{3}{2}\)x + \(\dfrac{1}{2}\)| = | 4x - 1 |
2, | \(\dfrac{5}{4}\)x - \(\dfrac{7}{2}\) | - | \(\dfrac{5}{8}x+\dfrac{3}{5}\) | = 0
3, | \(\dfrac{7}{5}x+\dfrac{2}{3}\) | = | \(\dfrac{4}{3}x-\dfrac{1}{4}\) |
4, | \(\dfrac{7}{8}x+\dfrac{5}{6}\) | - | \(\dfrac{1}{2}x+5\) | = 0
Bài 12: Tìm giá trị nhỏ nhất của các biểu thức sau:
a) A=\(2,25-\dfrac{1}{4}\text{|1+2x|}\)
b) B=\(\dfrac{1}{3+\dfrac{1}{2}\text{|2x-3|}}\)
Giúp mình với mình đang cần gấp
\(|97\dfrac{2}{3}-125\dfrac{3}{5}|+97\dfrac{2}{5}-125\dfrac{1}{3}\)
Tìm GTNN của biểu thức sau:
a. B = \(\left|x+\dfrac{1}{2}\right|+\left|x+\dfrac{1}{3}\right|+\left|x+\dfrac{1}{4}\right|\)
b. \(C=3\left|x+-\dfrac{2}{5}\right|+\dfrac{5}{7}\)
Giúp với!
