1/1X5+1/5X9+1/9X13+.+1/2005X2009

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1/1X5+1/5X9+1/9X13+.+1/2005X2009
1/1X5+1/5X9+1/9X13+.+1/2005X2009

1/1X5+1/5X9+1/9X13+.+1/2005X2009
1/1X5+1/5X9+1/9X13+.+1/2005X2009
=(1/4)×(1-1/5+1/5-1/9+1/9-1/13+...+1/2005-1/2009)
=(1/4)×(1-1/2009)
=(1/4)×2008/2009
=502/2009

=1/4(1-1/5+1/5-1/9******+1/2005-1/2009)
=(1-1/2009)/4
=502/2009

1/2005X2009=1/4(1/2005-1/2009)
你每个这样写,提取1/4相加
1/4(1-1/2009)=502/2009

=1/4(1-1/5+1/5-1/9******+1/2005-1/2009)
=(1-1/2009)/4
=502/2009

4((5-1)/1x5加(9-5)/5x9……)=4x(1-1/2009)=4032/2009