1/2+5/6+11/12+19/20+.+89/90+109/116等于多少?需要具体的步骤,

网友回答

1/2+5/6+11/12+19/20+.+89/90+109/110
=(1-1/2)+(1-1/6)+(1-1/12)+(1-1/20)+……+(1-1/110)
=10-1/(1*2)-1/(2*3)-1/(3*4)-……-1/(10*11)
=10-(1-1/2+1/2-1/3+1/3-1/4+……+1/10-1/11)
=10-(1-1/11)
=10-10/11
=100/11