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)(b-2005)的值](/uploads/image/z/14578259-59-9.jpg?t=%E9%98%85%E8%AF%BB1%2F1%2A2%3D1-1%2F2%2C1%2F2%2A3%3D1%2F2-1%2F3%2C1%2F3%2A4%3D1%2F3-1%2F4...%E8%AF%BA%2Fa-1%2F%2B%2Fab-2%3D0%E8%AF%95%E6%B1%821%2Fab%2B1%2F%28a%2B1%29%28b%2B1%29%2B1%2F%28a%2B2%29%28b%2B2%29.1%2Fa%2B%282005%29%28b-2005%29%E7%9A%84%E5%80%BC)
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