1/1*2+1/2*3+1/3*4...1/19*20=?

1+2+3+4. 1+2+3+4. 1+2+3+4.+1000 1+2+3+4.+101 1+2+3+4..100000000 1+2+3+4.= 1+1+2+3+4.+99 1+2+3+4.=1/12? 1/1+2+1/1+2+3+1/1+2+3+4+...+1/1+2+3+4...+992+1分之1加1+2+3/1这样 1/1*2+1/2*3+1/3*4.+1/2011*2012+1/2012*2013 1/1*2+1/2*3+1/3*4...+1/99*100+1/(2011*2012) （1-1/2-1/3-1/4..-1/2004)*(1+1/2+1/3+1/4+...+1/2005)-(1-1/2-1/3-1/4-...-1/2005)*(1+1/2+1/3+1/4+...+1/2004) (1)计算1/1*2+1/2*3+1/3+4.+1/99*100 (2)1/1*3+1/3*5+1/5*7.+1/49*51 1/1*2+1/2*3+1/3*4...1/19*20=? 1/1乘2+1/2乘3+1/3乘4.+1/199乘200 1/1*2+1/2*3+1/3*4.+1/2003*2004 1/1×2+1/2×3+1/3×4...+1/2006×2007=? 1/1*2+1/2*3+1/3*4.+1/99*100这道题怎么做