阅读1/1*2=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4...诺/a-1/+/ab-2=0试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2).1/a+(2005)(b-2005)的值

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阅读1/1*2=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4...诺/a-1/+/ab-2=0试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2).1/a+(2005

阅读1/1*2=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4...诺/a-1/+/ab-2=0试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2).1/a+(2005)(b-2005)的值
阅读1/1*2=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4...诺/a-1/+/ab-2=0试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)
.1/a+(2005)(b-2005)的值

阅读1/1*2=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4...诺/a-1/+/ab-2=0试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2).1/a+(2005)(b-2005)的值
∵/a-1/+/ab-2/=0
∴ a-1=0 ab-2=0 解得 a=1 b=2
1/ab+1/(a+1)(b+1)+...1/(a+2005)(b+2005)=1/(1x2)+1/(2x3)+1/(3x4)...1/(2006)(2007)
=1-1/2+1/2-1/3+1/3-1/4...1/2006-1/2007=1-1/2007=2006/2007

∵/a-1/+/ab-2/=0
∴ a-1=0 ab-2=0 解得 a=1 b=2
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2) +……+1/(a+2005)(b+2005)
=1/1×2 + 1/2×3 + 1/3×4+……+1/2006×2007
=1- 1/2 + 1/2 -1/3 +1/3 -1/4+……+1/2006-1/2007
=1 - 1/2007
=2006/2007