已知a=14,b=2.求1/ab+1/(a+1)(b+1)+...+1/(a+2004)(b+2004)的值

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已知a=14,b=2.求1/ab+1/(a+1)(b+1)+...+1/(a+2004)(b+2004)的值已知a=14,b=2.求1/ab+1/(a+1)(b+1)+...+1/(a+2004)(b

已知a=14,b=2.求1/ab+1/(a+1)(b+1)+...+1/(a+2004)(b+2004)的值
已知a=14,b=2.求1/ab+1/(a+1)(b+1)+...+1/(a+2004)(b+2004)的值

已知a=14,b=2.求1/ab+1/(a+1)(b+1)+...+1/(a+2004)(b+2004)的值
1/ab+1/(a+1)(b+1)+...+1/(a+2004)(b+2004)
=(1/12)(1/2-1/14+1/3-1/15+.+1/2006-1/2018)
=(1/12)(1/2-1/14+1/3-1/15+.+1/2006-1/2018)
=(1/12){(1/2+1/3+...+1/2004}-1/14-1/15-...-1/2018)
=(1/12)(1/2+1/3+...+1/13-1/2007-1/2008-...-1/2018)
=(1/12)(1/2+1/3+...+1/13-12/2012)
=0.188

1/ab+1/(a+1)(b+1)+...+1/(a+2004)(b+2004)
=(1/12)(1/2-1/14+1/3-1/15+.....+1/2006-1/2018)
=(1/12)(1/2-1/14+1/3-1/15+.....+1/2006-1/2018)
=(1/12)(1/2+1/3+...+1/13-1/2007-1/2008-...-1/2018)

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