116问答网 > 1⼀3＋1⼀15＋1⼀35＋1⼀63＋1⼀99＋1⼀143＋1⼀195＋1⼀255 =

1⼀3＋1⼀15＋1⼀35＋1⼀63＋1⼀99＋1⼀143＋1⼀195＋1⼀255 =

2025-06-26 13:22:39

推荐回答（3个）

回答1：

1/（1x3）+1/（3x5）+1/（5x7）+1/（7x9）+1/（9x11）+1/（11x13）+1/（13x15）+1/（15x17）
=(1-2/3)+(2/3-3/5)+(3/5-4/7)+(4/7-5/9)+(5/9-6/11)+(6/11-7/13)+(7/13-8/15)+ (8/15-9/17)
＝1-9/17
＝8/17

方法二:

3=1*3 15=3*5 35=5*7 63=7*9 99=9*11 143=11*13 195=13*15 255=15*17 就是把分母拆开,1/2[(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)+(1/11-1/13)+(1/13-1/15)+(1/15-1/17)]=1/2[1-(1/17)]=8/17

回答2：

1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+1/2(1/7-1/9)+1/2(1/9-1/11)+1/2(1/11-1/13)+1/2(1/13-1/15)+1/2(1/15-1/17)=1/2(1-1/17)=8/17 故应选C

回答3：

1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+1/2(1/7-1/9)+1/2(1/9-1/11)+1/2(1/11-1/13)+1/2(1/13-1/15)+1/2(1/15-1/17)=1/2(1-1/17)=8/17 所以选C