Bài 10: Chứng Minh Rằng (CMR)

A = \(\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2+\left(\dfrac{1}{2}\right)^3+...+\left(\dfrac{1}{2}\right)^{99}< 1\)

B= \(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{99}}< \dfrac{1}{2}\)

Bài 24: Tính

14. \(\left(\dfrac{1}{7}\right)^2.\dfrac{1}{7}.49^2\)

15. \(\left(\dfrac{4}{9}+\dfrac{1}{3}\right)^2\)

Bài 24: Tính

11. \(25.5^3.\dfrac{1}{625}.5^2\)

12. \(4.32:\left(2^3.\dfrac{1}{16}\right)\)

13. \(5^2.3^5.\left(\dfrac{3}{5}\right)\)

Bài 24: Tính

2. \(\left(0,125^3\right).512\)

3. \(\left(0,25^4\right).1024\)

4. \(\dfrac{90^3}{15^3}\)

5. \(\dfrac{790^4}{79^4}\)

Tính thuận tiện

2, \(\dfrac{5}{7}.\dfrac{5}{11}+\dfrac{5}{7}.\dfrac{2}{11}-\dfrac{5}{7}\)

Tính thuận tiện

3, \(\left(\dfrac{1}{99}+\dfrac{12}{999}-\dfrac{123}{9999}\right).\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{6}\right)\)

4, \(\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+...+\dfrac{2}{97.99}\)

5, \(\dfrac{3}{5.7}+\dfrac{3}{7.9}+\dfrac{3}{9.11}+...+\dfrac{3}{59.61}\)