Question

so sánh (1-1/4).(1-1/9).(1-1/16)....(1-1/100) với 11/19

Answer 1

Đặt A= ( 1-\(\frac{1}{4}\)). ( 1-\(\frac{1}{9}\)).( 1-\(\frac{1}{16}\))......(1-\(\frac{1}{100}\))

Ta có:A= ( 1-\(\frac{1}{4}\)). ( 1-\(\frac{1}{9}\)).( 1-\(\frac{1}{16}\))......(1-\(\frac{1}{100}\))

A = \(\frac{3}{4}\).\(\frac{8}{9}\).\(\frac{15}{16}\).......\(\frac{99}{100}\)

A= \(\frac{1.3}{2.2}\). \(\frac{2.4}{3.3}\).\(\frac{3.5}{4.4}\).......\(\frac{9.11}{10.10}\)

A=\(\frac{1.2.3....9}{2.3.4....10}\).\(\frac{3.4.5....11}{2.3.4....10}\)

A= \(\frac{1}{10}\). \(\frac{11}{2}\)

A= \(\frac{11}{20}\)

Do 20> 19 => \(\frac{11}{20}\)< \(\frac{11}{19}\). Vậy A< \(\frac{11}{19}\)

Duyệt đi, chúc bạn học giỏi!

Answer 2

cách k ở đâu vậy