计算：1/1x3+1/3x5+1/5x7+.+1/31x33+1/33x35,

来源：学生作业帮编辑：拍题作业网作业帮分类：数学作业时间：2024/04/28 04:10:16

因为 an=1/[(2n-1)*(2n+1)] = 1/2 [1/(2n-1) - 1/(2n+1)]
所以,
1/1x3+1/3x5+1/5x7+.+1/31x33+1/33x35
= 1/2*[(1/1 - 1/3) + (1/3 - 1/5) + (1/5 - 1/7) + …… + (1/33 - 1/35)]
= 1/2*(1/1 - 1/35)
=1/2* 34/35
=17/35
再问：可以简便些吗，讲解
再答：因为 1/1 - 1/3 = 3/3 - 1/3 = 2/3 = 2×1/3 所以，1/(1×3) = 1/2 × (1/1 - 1/3) 同理，1/3 - 1/5 = 5/15 - 3/15 = 2/15 = 2 × 1/15 所以，1/(3×5) = 1/2×(1/3 - 1/5) ………… 1/(33×35) = 1/2×(1/33 - 1/35) 代到公式中，你会发现放多分数都会正、负抵消，只剩下 1 和 -1/35 所以得到最终结果。

计算：1/1x3+1/3x5+1/5x7+...1/2009x2011+1/2011×2013 1/1x3+1/3x5+1/5x7+.+1/1997x1999 简便计算. 计算1/1X3+1/3x5十1/5X7+.+1/2009x2011 计算：1/1x3+1/3x5+1/5x7+1/7x9+……+1/2011x2013 x8+x7+x6+x5+x4+x3+x2+x+1因式分解 1/1X3+1/3X5+1/5X7...1/17X19+1/19X21= 1/1x3+1/3x5+1/5x7.1/2009x2010+1/2011x2013 1/1x3+1/3x5+1/5x7+1/7x9+1/9x11=? 1/1x3+1/3x5+1/5x7+……+1/99x101 1/1x3+1/3x5+1/5x7+…+1/2011x2013是多少? 1/(1x3)+1/(3x5)+1/(5x7)+.+1/(2011x2013) 等于什么 1/1x3+1/3x5+1/5x7+.+1/2009x2011=