Question

Chứng minh rằng:  A = 1 12 + 1 13 + 1 14 + ... + 1 22 > 1 2

Answer 1

A = 1 12 + 1 13 + 1 14 + ... + 1 22 > 1 2 ⇔ 1 12 + 1 13 + 1 14 + ... + 1 22 > 11 22 ⇔ 1 12 − 1 22 + 1 13 − 1 22 + 1 14 − 1 22 + ... + 1 22 − 1 22 > 0

Vì  1 12 > 0 , 1 13 > 0 , ... , 1 21 > 1 22 nên  1 12 − 1 22 > 0 , 1 13 − 1 22 > 0 , ... , 1 21 − 1 22 > 0 , 1 22 − 1 22 = 0

Suy ra  A > 1 2