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1/1X2=1-1/21/2+3=1/2-1/31/3+4=1/3-1/4.1/1X2=1-1/21/2+3=1/2-1/31/3+4=1/3-1/4.（3）若1/1X3+1/3X5+1/5X7+.+1/（2n-1）(2n+1)的值为17/35,求n的值
题目详情
1/1X2=1-1/2 1/2+3=1/2-1/3 1/3+4=1/3-1/4 .
1/1X2=1-1/2 1/2+3=1/2-1/3 1/3+4=1/3-1/4 .
（3）若1/1X3+1/3X5+1/5X7+.+1/（2n-1）(2n+1)的值为17/35,求n的值
1/1X2=1-1/2 1/2+3=1/2-1/3 1/3+4=1/3-1/4 .
（3）若1/1X3+1/3X5+1/5X7+.+1/（2n-1）(2n+1)的值为17/35,求n的值
▼优质解答
答案和解析
1/(1×3)+1/(3×5)+...+1/[(2n-1)(2n+1)]
=(1/2)[1-1/3+1/3-1/5+...+1/(2n-3)-1/(2n-1)+1/(2n-1)-1/(2n+1)]
=(1/2)[1-1/(2n+1)]
=n/(2n+1)=17/35
n=17
=(1/2)[1-1/3+1/3-1/5+...+1/(2n-3)-1/(2n-1)+1/(2n-1)-1/(2n+1)]
=(1/2)[1-1/(2n+1)]
=n/(2n+1)=17/35
n=17
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