Question

[Trần Quang Hiếu]

bài 3: chứng tỏ rằng:

b) Đặt A = \(\frac{1}{15.18}+\frac{1}{18.21}+...+\frac{1}{87.90}

Answer 1

[Phương Thảo]

Ta có: \(A=\frac{1}{15.18}+\frac{1}{18.21}+...+\frac{1}{87.90}\)

                \(=\frac{1}{3}(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{87}-\frac{1}{90})\)

                \(=\frac{1}{3}(\frac{1}{15}-\frac{1}{90})\)

                \(=\frac{1}{3}(\frac{6}{90}-\frac{1}{90})\)

                \(=\frac{1}{3}.\frac{5}{90}\)

                \(=\frac{1}{54}\)

Ta có: 1= \(\frac{54}{54}\)

Suy ra A < 1 (đpcm)

Answer 2

[Phạm Nguyễn Tất Đạt]

3A=3*(1/15*18+1/18*21+...+1/87*90)

3A=3/15*18+3/18*21+...+3/87*90

3A=1/15-1/18+1/18-1/21+...+1/87-1/90

3A=1/15-1/90

3A=1/18

A=1/18 chia3

A=1/54

vì 1/54<1 nên A<1