Tính nhanh tổng sau : A = $\dfrac{1}{2.15}$ + $\dfrac{1}{15.3}$ + $\dfrac{1}{3.21}$ + ... + $\dfrac{6}{87.90}$
2 câu trả lời
Ta có:
`A = 1/(2.15) + 1/(15.3) + 1/(3.21) +...+ 6/(87. 90)`
`1/6A = 1/(12. 15) + 1/(18. 15) +...+ 1/(87. 90)`
`1/6A = 1/3(3/(12.15) + 3/(15. 18) +...+ 3/(87. 90))`
`1/6A = 1/3(1/12 - 1/15 + 1/15 - 1/18 +...+ 1/87 - 1/90)`
`1/6A = 1/3(1/12 - 1/90)`
`1/6A = 1/3. 13/180`
`A = (1/3. 13/180)/(1/6)`
`A = 13/90`
Bạn viết lại biểu thức `A`
`= 6/(2.6.15) + 6/(3.6.15) + 6/(3.6.21)+...+6/(87.90)`
`= 6/(12 . 15)+6/(15 . 18) + 6/(18 . 21)+...+6/(87 . 90)`
`= 2 (3/(12 . 15)+3/(15.18) + 3/(18.21)+...+3/(87 . 90))`
`= 2 (1/12-1/15+1/15-1/18+1/18-1/21+...+1/87-1/90)`
`=2 (1/12 - 1/90)`
`=2 . 13/180`
`= 13/90`
Vậy `A=13/90`
