1/1X3+1/3X5+1/5X7+……+1/(2n-1)(2n+1)=?虽然我知道了答案是n/2n+1,

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1/1X3+1/3X5+1/5X7+……+1/(2n-1)(2n+1)=?虽然我知道了答案是n/2n+1,
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1/1X3+1/3X5+1/5X7+……+1/(2n-1)(2n+1)=?虽然我知道了答案是n/2n+1,
1/1X3+1/3X5+1/5X7+……+1/(2n-1)(2n+1)=?
虽然我知道了答案是n/2n+1,

1/1X3+1/3X5+1/5X7+……+1/(2n-1)(2n+1)=?虽然我知道了答案是n/2n+1,
1/1X3+1/3X5+1/5X7+……+1/(2n-1)(2n+1)
=1/2×[1-1/3+1/3-1/5+1/5-1/7+……+1/(2n-1)-1/(2n+1)]
=1/2×[1-1/(2n+1)]
=1/2×2n/(2n+1)
=n/(2n+1)

很简单1/(2n-1)(2n+1)=[1/(2n-1)-1/(2n+1)]*1/2,然后逐项相加就得到答案了