1/2²-1+1/3²-1+4²-1+……+100²-1=?急求答案,简便的.
问题描述：
1/2²-1+1/3²-1+4²-1+……+100²-1=?急求答案,简便的.
答
1/(2²-1)+1/(3²-1)+1/(4²-1)+……+1/(100²-1)=1/(1*3)+1/(2*4)+1/(3*5)+.+1/(99*101)=1/2*(1-1/3+1/2-1/4+1/3-1/5+.+1/99-1/101)=1/2*(1+1/2-1/100-1/101)=1/2*14949/10100=14949/20200