1/3+1/15+1/35+1/63+1/99+1/145+1/195+1/255

问题描述:

1/3+1/15+1/35+1/63+1/99+1/145+1/195+1/255

有两个数打错了吧 应该是143把整个式子乘二 第一项能拆成1-1/3 第二项能拆成1/3-1/5 依次类推最后一项是1/15-1/17原式=(1-1/17)/2=8/17

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+1/3-1/5+1/5-1/7+...1/15-1/17)=8/17