1/(|x3)+1/(3x5)+|/(5x7)+,..+1/(2n-1)(2n+1)=17/35,求n的值

题目

1/(|x3)+1/(3x5)+|/(5x7)+,..+1/(2n-1)(2n+1)=17/35,求n的值

答案

1/(|x3)+1/(3x5)+|/(5x7)+,..+1/(2n-1)(2n+1)
=[1/2]x[1/1-1/3+1/3-1/5+1/5-1/7+.+1/(2n-1)-1/(2n+1)]
=[1/2]x[1-1/(2n+1)]
=n/(2n+1)
=17/35
=>
n=17