已知:︱a-2︱+(b-1)²=0 试求:1/ab+1/(a+1)(b+1)+……+1/(a+2011)(b+2011)的值.最好用文字详细的解答,谢谢.
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![已知:︱a-2︱+(b-1)²=0 试求:1/ab+1/(a+1)(b+1)+……+1/(a+2011)(b+2011)的值.最好用文字详细的解答,谢谢.](/uploads/image/z/11423756-20-6.jpg?t=%E5%B7%B2%E7%9F%A5%EF%BC%9A%EF%B8%B1a-2%EF%B8%B1%2B%EF%BC%88b-1%EF%BC%89%26%23178%3B%3D0+%E8%AF%95%E6%B1%82%EF%BC%9A1%2Fab%2B1%2F%28a%2B1%29%28b%2B1%29%2B%E2%80%A6%E2%80%A6%2B1%2F%28a%2B2011%29%28b%2B2011%29%E7%9A%84%E5%80%BC.%E6%9C%80%E5%A5%BD%E7%94%A8%E6%96%87%E5%AD%97%E8%AF%A6%E7%BB%86%E7%9A%84%E8%A7%A3%E7%AD%94%2C%E8%B0%A2%E8%B0%A2.)
已知:︱a-2︱+(b-1)²=0 试求:1/ab+1/(a+1)(b+1)+……+1/(a+2011)(b+2011)的值.最好用文字详细的解答,谢谢.
已知:︱a-2︱+(b-1)²=0 试求:1/ab+1/(a+1)(b+1)+……+1/(a+2011)(b+2011)的值.
最好用文字详细的解答,谢谢.
已知:︱a-2︱+(b-1)²=0 试求:1/ab+1/(a+1)(b+1)+……+1/(a+2011)(b+2011)的值.最好用文字详细的解答,谢谢.
∵|a-2|+(b-1)²=0,∴a=2 b=1
∴1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2001)(b+2001)
=1/(2×1)+1/(3×2)+1/(4×3)+……+1/(2013×2012)
=1-1/2+1/2-1/3+1/3-1/4+……+1/2012-1/2013
=1-1/2013
=2012/2013