2/(1*3)+2/(3*5)+2/(5*7)+2/(7*9)+.+2/(95*97)+2/(97*99)=?
问题描述:
2/(1*3)+2/(3*5)+2/(5*7)+2/(7*9)+.+2/(95*97)+2/(97*99)=?
需求讲解
答
2/(1*3)+2/(3*5)+2/(5*7)+2/(7*9)+.+2/(95*97)+2/(97*99)
=(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+.+(1/95-1/97)+(1/97-1/99)
=1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+.+1/95-1/97+1/97-1/99
=1-1/99
=98/99