求证1+1/3^2+1/5^2+..+1/(2n-1)^2>7/6-1/2(2n+1)(n>1)
来源：学生作业帮助网 编辑：六六作业网 时间：2024/11/18 12:29:49
求证1+1/3^2+1/5^2+..+1/(2n-1)^2>7/6-1/2(2n+1)(n>1)求证1+1/3^2+1/5^2+..+1/(2n-1)^2>7/6-1/2(2n+1)(n>1)求证1+
求证1+1/3^2+1/5^2+..+1/(2n-1)^2>7/6-1/2(2n+1)(n>1)
求证1+1/3^2+1/5^2+..+1/(2n-1)^2>7/6-1/2(2n+1)(n>1)
求证1+1/3^2+1/5^2+..+1/(2n-1)^2>7/6-1/2(2n+1)(n>1)
1+1/3^2+1/5^2+……+1/(2n-1)^2
>1+1/(3*5)+1/(5*7)+……+1/(2n-1)(2n+1)
=1+(1/2)(1/3-1/5+1/5-1/7+……+1/(2n-1)-1/(2n+1))
=1+(1/2)*(1/3-1/(2n+1))
=(7/6)-1/2(2n+1),n>1
主要用到裂项公式：1/(a*b)=(1/(b-a))*(1/a-1/b),a