1/13+1/35···1/2007*2009=

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1/1*3+1/3*5···1/2007*2009=1/1*3+1/3*5···1/2007*2009=1/1*3+1/3*5···1/2007*2009=1/1*3+1/3*5···1/2007*2

1/1*3+1/3*5···1/2007*2009=
1/1*3+1/3*5···1/2007*2009=

1/1*3+1/3*5···1/2007*2009=
1/1*3+1/3*5···1/2007*2009
=1/2×（1-1/3+1/3-1/5+……+1/2007-1/2009）
=1/2×（1-1/2009）
=1/2×2008/2009
=1004/2009

原式
=sum_{k=1}^{1004} 1/(2k-1)/(2k+1)
=sum_{k=1}^{1004} [1/(2k-1)-1/(2k+1)] /2
=[sum_{k=1}^{1004} 1/(2k-1) - sum_{k=1}^{1004} 1/(2k+1)] /2
=[1-1/2009]/2
=1004/2009.

1 2 3 4 ·····7 ·······10 ········?1 3 5 7 ·····?······?··········290 1 4 9 ·····?······?··········? 1+3+5+7+···+2005+2007+2009等于多少?要有过程····快····· 计算：1-2+3-4+5-6+·····+2007-2008的结果 1×3分之1+3×5分之1+···＋2007×2009分之1 1/1*3+1/3*5···1/2007*2009= (1+3+5······+2007+2009+2011)-(2+4+6+·····+2006+2008+2010) 计算：1/1×3+1/3×5+1/5×7+······+1/2005×2007（写清过程理由答案）急·····················1+2+3+...+999=? 证明1·3·5·····(2n-1)/2·4·6·····2n 2/(x+1)(x+3)+2/(x+3)(x+5)+·····+2/(x+2007)(x+2009) 计算1-3+5-7+9-11+··········+97-99= 1+2+3+4+5····+50 变态数学题·······方程一道············x+2y+3z=1x=y+12x+3y+5z=2方程组············要过程············我解了之后总觉得无解····· 计算:1/1·5+1/3·7+1/5·9+···+1/21·25 1+2++3+··········+10000= 俗语和名句的填空1······,自知之明.2······,行必果.3工欲善其事,······.4临渊羡鱼,······.5非学无以广才,······.6······,福兮祸之所伏.7项庄舞剑,······.8······,人以群解方程：x/1*2+ x/2*3 +······+ x/2007*2008=2007 序列 1 2 3 4 5 6 ······ n 对应的数 1 3 6 10 21······?