1/1×3+1/3×5+1/5×7+1/7×9+…+1/(2n-1)(2n+1)的值(n为正整数）
问题描述：
1/1×3+1/3×5+1/5×7+1/7×9+…+1/(2n-1)(2n+1)的值(n为正整数）
答
裂项相加得
1/2×[1-1/3+1/3-1/5+...+1/(2n-1)-1/(2n+1)]
=[1-1/(2n+1)]/2
=n/(2n+1)
答
1/1×3+1/3×5+1/5×7+1/7×9+…+1/(2n-1)(2n+1)
=(1/2)×[1/1-1/3+1/3-1/5+……+1/(2n-1)-1/(2n+1)]
=(1/2)×[1-1/(2n+1)]
=n/(2n+1)