A = 8/3.7 + 8/7.11 + 8/11.15 + … + 8/97.101 Question A = 8/3.7 + 8/7.11 + 8/11.15 + … + 8/97.101 in progress 0 Môn Toán Đan Thu 9 months 2021-04-29T00:31:50+00:00 2021-04-29T00:31:50+00:00 2 Answers 0 views 0
Answers ( )
*Lời giải :
`A = 8/(3.7) + 8/(7.11) + 8/(11.15) + … + 8/(97 . 101)`
`⇔ A = 2 . [1/3 – 1/7 + 1/7 – 1/11 + 1/11 – 1/15 + .. .+ 1/97 – 1/101]`
`⇔ A = 2 [1/3 + (- 1/7 + 1/7 – 1/11 + 1/11 – 1/15 + .. .+ 1/97) – 1/101]`
`⇔ A = 2 . [1/3 – 1/101]`
`⇔ A = 2 . 98/303`
`⇔ A = 196/303`
Vậy `A = 196/303`
$\text{Đáp án + Giải thích các bước giải:}$
`A=(8)/(3.7)+(8)/(7.11)+(8)/(11.15)+…+(8)/(97.101)`
`=>(A)/(2)=(4)/(3.7)+(4)/(7.11)+(4)/(11.15)+…+(4)/(97.101)`
`=>(A)/(2)=(1)/(3)-(1)/(7)+(1)/(7)-(1)/(11)+(1)/(11)-(1)/(15)+…+(1)/(97)-(1)/(101)`
`=>(A)/(2)=(1)/(3)-(1)/(101)`
`=>(A)/(2)=(98)/(303)`
`=>A=(196)/(303)`