当n=17 求1/1x3+1/3x5+1/5x7+.+1/(2n-1)(2n+1)的值?
题目
当n=17 求1/1x3+1/3x5+1/5x7+.+1/(2n-1)(2n+1)的值?
答案
1/1x3+1/3x5+1/5x7+.+1/(2n-1)(2n+1)=1/2*(1-1/3)+1/2*(1/3-1/5)+...+1/2*[1/(2n-1) -1/(2n+1)]=1/2*[1-1/3+1/3-1/5+1/5+...-1/(2n+1)]=1/2*[1-1/(2n+1)]其中,n=17,所以,原式=1/2*(1-1/35)=17/35
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