Question

1又1/15+3又1/35+5又1/63+7又1/99+9又1/143+11又1/195

Answer 1

解
原式=1+1/15+3+1/35+5+1/63+7+1/99+9+1/143+11+1/195
=1+3+5+7+9+(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
=36+(1/3-1/5+1/5-1/7+...+1/13-1/15)*1/2
=36+(1/3-1/15)*1/2
=36又2/15

Answer 2

原式=1+1/15+3+1/35+5+1/63+7+1/99+9+1/143+11+1/195
=1+3+5+7+9+(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
=36+(1/3-1/5+1/5-1/7+...+1/13-1/15)*1/2
=36+(1/3-1/15)*1/2
=36又2/15

Answer 3

原式=1+3+5+7+9+11+1/(3*5)+1/(5*7)+1/(9*7)+1/(9*11)+1/(11*13)+1/(15*13)
=36+(1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15)*1/2
=36+(1/3-1/15)*1/2
=36+2/15

Answer 4

1又1/15+3又1/35+5又1/63+7又1/99+9又1/143+11又1/195
=1+1/15+3+1/35+5+1/63+7+1/99+9+1/143+11+1/195
=1+3+5+7+9+11+1/15+1/35+1/63+1/99+1/143+1/195
=36+1/3*1/5+1/5*1/7+1/7*1/9+1/9*1/11+1/11*1/13+1/13*1/15
=36+1/2*(1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15)
=36+1/2*(1/3-1/15)
=36又2/15