1*3/1+3*5/1+5*7/1+···+2013*2015/1=?1*3/1+3*5/1+5*7/1+7*9/1+···+2013*2015/1=?
问题描述:
1*3/1+3*5/1+5*7/1+···+2013*2015/1=?
1*3/1+3*5/1+5*7/1+7*9/1+···+2013*2015/1=?
答
1/(1*3)+1/(3*5)+1/(5*7)+……+1/(2013*2015)=1/2*(1-1/3)+1/2*(1/3-1/5)+1/2*(1/5-1/7)+……+1/2*(1/2013-1/2015)=1/2*(1-1/3+1/3-1/5+1/5-1/7+……+1/2013-1/2015) =1/2*(1-1/2015) ...