1/2+5/6+11/12+19/20+.+89/90+109/110 答案是多少,还有要写明这里有几项?
问题描述:
1/2+5/6+11/12+19/20+.+89/90+109/110 答案是多少,还有要写明这里有几项?
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+……+1-1/90+1-1/110
=10-(1/2+1/6+1/12+1/20+……+1/90+1/110)
=10-(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/9-1/10+1/10-1/11)
=10-(1-1/11)
=9+1/11
=9又1/11是哪十项啊?1/2+5/6+11/12+19/20+29/30+41/42+55/56+71/72+89/90+109/110 =1-1/2+1-1/6+1/1/12+1-1/20+……+1-1/90+1-1/110=10-(1/2+1/6+1/12+1/20+……+1/90+1/110)=10-(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/9-1/10+1/10-1/11)=10-(1-1/11)=9+1/11=9又1/11