Ta có : `A = 124 . ( 1/(1.1985) + 1/(2.1986) + .... +1/(16.2000) )`
`=124/1984 . ( 1 - 1/1985 + 1/2 - 1/986 +....+ 1/16 - 1/2000 )`
`=1/16 . [ (1+1/2+...+1/16) - ( 1/1985 + 1/1986+ .... + 1/2000 )`
Lại có :`B=1/(1.17) + 1/(2.18) + ....+1/(1984.2000)`
`=1/16 . [ (1 + 1/2 + .... + 1/16 ) + ( 1/17+1/18 +....+1/1984-1/17-1/18-...-1/1984 )-(1/1985 + 1/1986 +.... +1/200 ) ]`
`=1/16.[ ( 1+1/2+...+1/16 ) - (1/1985+1/1986+...+1/2000 ) ]`
`Do 1/16.[ ( 1+1/2+...+1/16 ) - (1/1985+1/1986+...+1/2000 ) ] = 1/16.[ ( 1+1/2+...+1/16 ) - (1/1985+1/1986+...+1/2000 ) ]`
`⇒ A = B`
Vậy , `A = B`