Question

[Trần Nguyễn Hoài Thư]

Cho A = 1 - \(\frac{1}{2}\) +\(\frac{1}{3}\)-\(\frac{1}{4}\)+\(\frac{1}{5}\)-\(\frac{1}{6}\)+...+\(\frac{1}{149}\)-\(\frac{1}{150}\) ; B = \(\frac{1}{76}\)+\(\frac{1}{77}\)+\(\frac{1}{78}\)+...+\(\frac{1}{150}\).

Tính \(\frac{A}{B}\)

Answer 1

[soyeon_Tiểubàng giải]

A = 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + ... + 1/149 - 1/150

A = (1 + 1/3 + 1/5 + ... + 1/149) - (1/2 + 1/4 + 1/6 + ... + 1/150)

A = (1 + 1/2 + 1/3 +1/4 + 1/5 + 1/6 + ... + 1/149 + 1/150 - 2.(1/2 + 1/4 + 1/6 + ... + 1/150)

A = (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + ... + 1/149 + 1/150) - (1 + 1/2 + 1/3 + ... + 1/75)

A =1/76 + 1/77 + 1/78 + ... + 1/150

=> A/B = 1