Ta có: \(B=\left(1+\dfrac{1}{2}\right)\left(1+\dfrac{1}{3}\right)\left(1+\dfrac{1}{4}\right)\cdot...\cdot\left(1+\dfrac{1}{99}\right)\)
\(=\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot\dfrac{5}{4}\cdot...\cdot\dfrac{100}{99}\)
\(=\dfrac{100}{2}=50\)
\(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)....\left(1-\dfrac{1}{99}\right)\)
\(\left(\dfrac{1}{2}+1\right).\left(\dfrac{1}{3}+1\right).\left(\dfrac{1}{4}+1\right).\cdot\cdot\cdot.\left(\dfrac{1}{99}+1\right)\) làm ơn giúp mình với
\(\dfrac{99}{100}:\left(\dfrac{1}{4}-\dfrac{1}{12}+\dfrac{1}{3}\right)-\left(\dfrac{-7}{5}\right)^2\)
\(\dfrac{13}{15}\cdot0,25\cdot3+\left(\dfrac{8}{15}-1\dfrac{19}{60}\right):1\dfrac{23}{24}\)
Tính:
a) A= \(\left(\dfrac{5}{6}-\dfrac{4}{5}\right).1\dfrac{1}{5}+\dfrac{3}{16}:\left(\dfrac{-1}{2}\right)^3\)
b) B= \(\dfrac{4}{17}.\left(7\dfrac{3}{4}-6\dfrac{1}{3}\right)+\left(5\dfrac{3}{4}-6.95\right):\left(-1\dfrac{3}{5}\right)\)
Tính hợp lí:
a) (100-9)(99-9)(98-9)...(1-9).
b) \(\left(1-\dfrac{1}{100}\right)\left(1-\dfrac{1}{99}\right)...\left(1-\dfrac{1}{2}\right)\)
c) \(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{99.100}\)
Cho A=\(\left(\dfrac{1}{2^2}-1\right)\)\(\left(\dfrac{1}{3^2}-1\right)\)\(\left(\dfrac{1}{4^2}-1\right)\)...\(\left(\dfrac{1}{2013^2}-1\right)\)\(\left(\dfrac{1}{2014^2}-1\right)\) và B= \(-\dfrac{1}{2}\)
Hãy so sánh A và B
Thực hiện phép tính:
1, \(\left(\dfrac{-1}{2}\right)^2.\left|+8\right|-\left(-\dfrac{1}{2}\right)^3:\left|-\dfrac{1}{16}\right|\)
2, \(\left|-0,25\right|-\left(-\dfrac{3}{2}\right)^2:\dfrac{1}{4}+\dfrac{3}{4}.2017^0\)
3, \(\left|\dfrac{2}{3}-\dfrac{5}{6}\right|.\left(3,6:2\dfrac{2}{5}\right)^3\)
4, \(\left|\left(-0,5\right)^2+\dfrac{7}{2}\right|.10-\left(\dfrac{29}{30}-\dfrac{7}{15}\right):\left(-\dfrac{2017}{2018}\right)^0\)
5, \(\dfrac{8}{3}+\left(3-\dfrac{1}{2}\right)^2-\left|\dfrac{-7}{3}\right|\)
1) Tính tổng C = \(\left(1-\dfrac{1}{2}\right)\).\(\left(1-\dfrac{1}{3}\right)\).\(\left(1-\dfrac{1}{4}\right)\).....\(\left(1-\dfrac{1}{2022}\right)\)
2) Cho tổng A = \(\dfrac{1}{3}\) - \(\dfrac{2}{3^2}\) + \(\dfrac{3}{3^3}\) - \(\dfrac{4}{3^4}\) +...+ \(\dfrac{99}{3^{99}}\) - \(\dfrac{100}{3^{100}}\). Chứng tỏ rằng A < \(\dfrac{3}{16}\)
Bài 5. Tìm \(y\) biết:
a) \(\left(y+\dfrac{1}{2}\right)+\left(y+\dfrac{1}{4}\right)+\left(y+\dfrac{1}{8}\right)+\left(y+\dfrac{1}{16}\right)=1\)
b) \(\left(y+\dfrac{1}{2}\right)+\left(y+\dfrac{1}{4}\right)+\left(y+\dfrac{1}{8}\right)+...+\left(y+\dfrac{1}{1024}\right)=1\)
