如何解:1/(1*3)+1/(3*5)+1/(5*7)+···+1/(2009*2011)

问题描述:

如何解:1/(1*3)+1/(3*5)+1/(5*7)+···+1/(2009*2011)

1/(1*3)+1/(3*5)+1/(5*7)+···+1/(2009*2011)=1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+.+1/2(1/2009-1/2011)=1/2(1-1/3+1/3-1/5+1/5-1/7+.+1/2009-1/2011)=1/2(1-1/2011)=1/2 * 2010/2011=1005/2011...