1⼀2+5⼀6+11⼀12+19⼀20+29⼀30+......+9701⼀9702+9899+9900=??????

2024-12-25 03:06:00
推荐回答(1个)
回答1:

相邻分母间的差值依次为4,6,8,10,...,198.
由此可知上式共有99项
所以
1/2+5/6+11/12+19/20+29/30+......+9701/9702+9899/9900=
99-(1/2+1/6+1/12+1/20+1/30+......+1/9702+1/9900)=
99-(1/2+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+......+(1/98-1/99)+(1/99-1/100))=
99-(1/2+1/2-1/100)=
9801/100