Tính
a)\(5^2-\left(-5\right)^3+\frac{1}{2}-\left(\frac{1}{2}\right)^2\)
b)\(2\frac{3}{4}-\frac{1}{8}\cdot1\frac{1}{2}\)
c)\(\left(\frac{1}{3^5}+\frac{1}{3^6}+\frac{1}{3^7}+\frac{1}{3^8}\right)\cdot3^9\)
d)\(\left(\frac{1}{2^2}-1\right)\cdot\left(\frac{1}{3^2}-1\right)\cdot\cdot\cdot\cdot\left(\frac{1}{100^2}-1\right)\)
\(\left[6\cdot\left(-\frac{1}{3}\right)^2-3\cdot\left(-\frac{1}{3}\right)+1\right]:\left(-\frac{1}{3}-1\right)\)
\(\frac{\left(\frac{2}{3}\right)^3\cdot\left(-\frac{3}{4}\right)^2\cdot\left(-1\right)^{2003}}{\left(\frac{2}{5}\right)^2\cdot\left(-\frac{5}{12}\right)^3}\)
Tính
a)\(\left(-\frac{1}{4}\right)^2+\frac{3}{8}\cdot\left(-\frac{1}{6}\right)-\frac{3}{16}:\left(-\frac{1}{2}\right)\)
b)\(-\frac{1}{2}:\left(1-\frac{3}{4}\right)^2-\frac{2}{3}:\frac{9}{8}-\left(\frac{9}{8}\right)^0\)
c)\(4\cdot\left(-\frac{1}{2}\right)^3+2\cdot\left(-\frac{1}{2}\right)^2-3\cdot\left(-\frac{1}{2}\right)+2006^0\)
Tính giá trị của biểu thức:
a,(32)2-(-23)2-(-52)3
b,\(\left|\frac{-1}{2}\right|^2\cdot\left(-32\right)-\left(-8\right)+\left|\frac{1}{2}\right|^3\)
c,\(2^3+3\cdot\left(\frac{-5}{86}\right)^0\cdot\left(\frac{1}{2}\right)^2\cdot4+\left[\left(-2\right)^2:\frac{1}{2}\right]:8\)
d,\(\left|\frac{5}{7}\cdot\left(-14\right)\right|-\left(\frac{2}{3}\right)^2\cdot\left(-18\right)+6^2\cdot\frac{-1}{18}\)
tình hợp lí:
\(\frac{\left(\frac{1}{5}-\frac{2}{7}\right)\cdot\frac{3}{4}-\frac{3}{4}\cdot\left(\frac{1}{3}-\frac{2}{7}\right)}{\frac{1}{5}\cdot\frac{2}{7}-\frac{1}{3}\cdot\left(\frac{2}{7}+\frac{3}{9}\right)+\frac{3}{9}+\frac{1}{5}}\)
Tính các tích sau: với n là số tự nhiên, n<3
a) \(\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot...\cdot\left(1-\frac{1}{n}\right)\)
b) \(\left(1-\frac{1}{2^2}\right)\cdot\left(1-\frac{1}{3^2}\right)\cdot\left(1-\frac{1}{4^2}\right)\cdot...\cdot\left(1-\frac{1}{n^2}\right)\)
tinh hop li :
\(\frac{\left(\frac{1}{5}-\frac{2}{7}\right)\cdot\frac{3}{4}-\frac{3}{4}\cdot\left(\frac{1}{3}-\frac{2}{7}\right)}{\frac{1}{5}\cdot\frac{2}{7}-\frac{1}{3}\cdot\left(\frac{2}{7}+\frac{3}{9}\right)+\frac{3}{9}+\frac{1}{5}}\)
\(\frac{\left(-\frac{1}{2}\right)^3-\left(\frac{3}{4}\right)^3\cdot\left(-2\right)^2}{2\cdot\left(-1\right)^5+\left(\frac{3}{4}\right)^2-\frac{3}{8}}\)
\(\frac{\left(1+2+...+100\right)\cdot\left(\frac{1}{3}-\frac{1}{5}-\frac{1}{7}-\frac{1}{9}\right)\cdot\left(6,3\cdot12-21\cdot3,6\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}\)
\(C=\left(1-\frac{2}{2\cdot3}\right)\cdot\left(1-\frac{2}{3\cdot4}\right)\cdot\left(1-\frac{2}{4\cdot5}\right)\cdot....\cdot\left(1-\frac{2}{99\cdot100}\right)\)
