求证1+1⼀3^2+1⼀5^2+..+1⼀(2n-1)^2>7⼀6-1⼀2(2n+1)(n>1)

2025-03-09 22:46:57
推荐回答(1个)
回答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有不懂欢迎追问