若1/(1×3)+1/(3×5)+1/(5×7)+……+1/(2n-1)(2n+1)的值为17/35,求n的值

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若1/(1×3)+1/(3×5)+1/(5×7)+……+1/(2n-1)(2n+1)的值为17/35,求n的值
若1/(1×3)+1/(3×5)+1/(5×7)+……+1/(2n-1)(2n+1)的值为17/35,求n的值

若1/(1×3)+1/(3×5)+1/(5×7)+……+1/(2n-1)(2n+1)的值为17/35,求n的值
即1/2×(1-1/3)+1/2×(1/3-1/5)+……+1/2×[1/(2n-1)-1/(2n+1)]=17/35
1/2×[1-1/3+1/3-1/5+……+1/(2n-1)-1/(2n+1)]=17/35
1/2×[1-1/(2n+1)]=17/35
n/(2n+1)=17/35
所以35n=17(2n+1)
35n=34n+17
n=17

提示一下:1/(2n-1)(2n+1)=1/2* 【1/(2n-1)-1/(2n+1)]
原始变成 1/2*[1-1/(2n+1)]=17/35

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