请问(1/2+1/3+.+1/2003)*(1-1/2-3/1.1/2003)*(1/2+1/3.+1/2004)等于多少?
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![请问(1/2+1/3+.+1/2003)*(1-1/2-3/1.1/2003)*(1/2+1/3.+1/2004)等于多少?](/uploads/image/z/7621792-16-2.jpg?t=%E8%AF%B7%E9%97%AE%281%2F2%2B1%2F3%2B.%2B1%2F2003%29%2A%281-1%2F2-3%2F1.1%2F2003%EF%BC%89%2A%EF%BC%881%2F2%2B1%2F3.%2B1%2F2004%29%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%3F)
请问(1/2+1/3+.+1/2003)*(1-1/2-3/1.1/2003)*(1/2+1/3.+1/2004)等于多少?
请问(1/2+1/3+.+1/2003)*(1-1/2-3/1.1/2003)*(1/2+1/3.+1/2004)等于多少?
请问(1/2+1/3+.+1/2003)*(1-1/2-3/1.1/2003)*(1/2+1/3.+1/2004)等于多少?
解
令a=1/2+1/3+.+1/2002,则原式变为
(a+1/2003)*(1+a)-(1+a+1/2003)*a
=a+a ²+1/2003+1/2003a-(a+a ²+1/2003a)
=1/2003
换元法