1/3+1/15+1/35+1/63+1/99+1/143+1/195+1/255 =
来源:百度知道 编辑:UC知道 时间:2024/06/08 00:44:02
1/3+ 1/15+ 1/35 +1/63 + 1/99+ 1/143+ 1/195+ 1/255的值是:
A、6/17 B、6/19 C、8/17 D、8/19
谁知道简便方法是什么啊?怎么快速算出来呢?
A、6/17 B、6/19 C、8/17 D、8/19
谁知道简便方法是什么啊?怎么快速算出来呢?
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
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
上式可化简为1/2[1-1/3+1/3-1/5+1/5-1/7+1/7-````=1/2(1-1/17)=8/16
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
C,裂项法
1+1/2+1/3+.......+1/n=?
1+1/2+1/3+1/4...+1/n=?
1-1/3-1/5+1/3-1/5-1/7+1/5-1/7-1/9……+1/2003-1/2005-1/2007
1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+......+1/100 = ?
(1-1/2)+(1/2-1/3)+(1/3-1/4)+..(1/2001-1/2002) 1/1x2+1/2x3+1/3x4+..+1/2001x2002
1×1/2+2×1/3+3×1/4+4×1/5+5×1/6+……98×1/99+99×1/100
1+1/(1+2)+1/(1+2+3)+…+1/(1+2+3+…+n)
1+1/(1+2) 1/(1+2+3)……+1/(1+2+3……+100)
1/1×2×3+1/2×3×4+1/3×4×5···+1/98×99×100
(1+1/2)(1+1/3+(1+1/4)……(1+1/100)/(1-1/2)(1-1/3)(1-1/4)……(1-1/100)