1/1*5+1/3*7+1/5*9+.+1/(2n-1)(2n+3)
问题描述：
1/1*5+1/3*7+1/5*9+.+1/(2n-1)(2n+3)
答
1/(2n-1)(2n+3)=1/4[1/(2n-1)-1/(2n+3)]
原式=1/4[1-1/(2n+3)]=1/4-1/4(2n+3)
答
1/1*5+1/3*7+1/5*9+.+1/(2n-1)(2n+3)
=【（1-1/5+1/3-1/7+1/5-1/9+.+1/(2n-1)-1/(2n+3) 】÷4
=【1+1/3-1/（2n+1)-1/(2n+3)】÷4
=1/3-（n+1)/[(2n+1)(2n+3)]