1994 + 1 / 2 - (1 + 1 / 3) + (2 + 1 / 2) - (3 + 1 / 3) + (4 + 1 / 2) - (5 + 1 / 3) +. + (1992 + 1 / 2) - (1993 + 1 / 3) I can't understand the formula by writing

1994 + 1 / 2 - (1 + 1 / 3) + (2 + 1 / 2) - (3 + 1 / 3) + (4 + 1 / 2) - (5 + 1 / 3) +. + (1992 + 1 / 2) - (1993 + 1 / 3) I can't understand the formula by writing

1994+1/2-(1+1/3)+(2+1/2)-(3+1/3)+(4+1/2)-(5+1/3)+.+(1992+1/2)-(1993+1/3)
=-(1+1/3)+(2+1/2)-(3+1/3)+(4+1/2)-(5+1/3)+.+(1992+1/2)-(1993+1/3)+（1994+1/2）
=-1-1/3+2+1/2-3-1/3+4+1/2-5-1/3+.+1992+1/2-1993-1/3+1994+1/2
=（-1+2-3+4-5+… +1992-1993+1994）+（-1/3+1/2-1/3+1/2-1/3+… +1/2-1/3+1/2）
=【（-1+2）+（-3+4）+… +（-1993+1994）】+（-1/3-1/3-… -1/3）+（1/2+1/2+… +1/2）
=1994/2+（-1/3）*（1994/2）+（1/2*1994/2）
=997-997/3+997/2
=1163 and 1 / 6