1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11).1/(97x99)=多少?这个肯定得用简便方法,请指教.
问题描述：
1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11).1/(97x99)=多少?这个肯定得用简便方法,请指教.
答
您好
1/(1x3) =(1-1/3)/2
那么1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11).1/(97x99)
=（1-1/3)/2+（1/3-1/5)/2+(1/5-1/7)/2+.+(1/97-1/99)/2
=(1-1/3+1/3-1/5+1/5-1/7+.-1/97+1/97-1/99)/2
=(1-1/99)X2
=49/99