0 bình luận về “1/1x2x3 + 1/2x3x4+1/3x4x5 + … + 198x99x100= X/19 800
tìm x”
`1/(1 xx 2 xx 3) + 1/(2 xx 3 xx 4) + 1/ (3 xx 4 xx 5) + … + 1/(98 xx 99 xx 100) = x/19800`
`⇒ 2 xx (1/(1 xx 2 xx 3) + 1/(2 xx 3 xx 4) + 1/ (3 xx 4 xx 5) + … + 1/(98 xx 99 xx 100) ) = 2 xx x/19800` `⇒ 2/(1 xx 2 xx 3) + 2/(2 xx 3 xx 4) + 2/ (3 xx 4 xx 5) + … + 2/(98 xx 99 xx 100) = x/9900` `⇒ 1/2 – 1/(2 xx 3) + 1/(2 xx 3) – 1/(3 xx 4) + 1/(3 xx 4) – 1/(4 xx 5) + … + 1/(98 xx 99) – 1/(99 xx 100) = x/9900`
`1/(1 xx 2 xx 3) + 1/(2 xx 3 xx 4) + 1/ (3 xx 4 xx 5) + … + 1/(98 xx 99 xx 100) = x/19800`
`⇒ 2 xx (1/(1 xx 2 xx 3) + 1/(2 xx 3 xx 4) + 1/ (3 xx 4 xx 5) + … + 1/(98 xx 99 xx 100) ) = 2 xx x/19800`
`⇒ 2/(1 xx 2 xx 3) + 2/(2 xx 3 xx 4) + 2/ (3 xx 4 xx 5) + … + 2/(98 xx 99 xx 100) = x/9900`
`⇒ 1/2 – 1/(2 xx 3) + 1/(2 xx 3) – 1/(3 xx 4) + 1/(3 xx 4) – 1/(4 xx 5) + … + 1/(98 xx 99) – 1/(99 xx 100) = x/9900`
`⇒ 1/2 – 1/(99 xx 100) = x/9900`
`⇒ 4950/9900 – 1/9900 = x/9900`
`⇒ 4949/9900 = x/9900`
`⇒ x = 4949`
`Vậy x = 4949`
Đáp án + Giải thích các bước giải:
`1/(1xx2xx3)+1/(2xx3xx4)+1/(3xx4xx5)+…+1/(98xx99xx100)=x/19800`
`=>1/2(2/(1xx2xx3)+2/(2xx3xx4)+2/(3xx4xx5)+…+2/(98xx99xx100))=x/19800`
`=>1/2(1/(1xx2)-1/(2xx3)+1/(2xx3)-1/(3xx4)+1/(3xx4)-1/(4xx5)+…+1/(98xx99)-1/(99xx100))=x/19800`
`=>1/2(1/(1xx2)-1/(99xx100))=x/19800`
`=>1/2(1/2-1/9900)=x/19800`
`=>1/2(4950/9900-1/9900)=x/19800`
`=>1/2xx4949/9900=x/19800`
`=>4949/19800=x/19800`
`=>x=4949`
Vậy `x=4949`