如果有理数a、b满足丨a-2丨+(1-b)²=0?试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2010)(b+2010)的值.(提示:1/2×3=1/2-1/3,1/3×4=1/3-1/4^)
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![如果有理数a、b满足丨a-2丨+(1-b)²=0?试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2010)(b+2010)的值.(提示:1/2×3=1/2-1/3,1/3×4=1/3-1/4^)](/uploads/image/z/2770412-68-2.jpg?t=%E5%A6%82%E6%9E%9C%E6%9C%89%E7%90%86%E6%95%B0a%E3%80%81b%E6%BB%A1%E8%B6%B3%E4%B8%A8a-2%E4%B8%A8%2B%EF%BC%881-b%EF%BC%89%26%23178%3B%3D0%3F%E8%AF%95%E6%B1%821%2Fab%2B1%2F%28a%2B1%29%28b%2B1%29%2B1%2F%28a%2B2%29%28b%2B2%29%2B%E2%80%A6%2B1%2F%28a%2B2010%29%28b%2B2010%29%E7%9A%84%E5%80%BC.%EF%BC%88%E6%8F%90%E7%A4%BA%EF%BC%9A1%2F2%C3%973%3D1%2F2-1%2F3%2C1%2F3%C3%974%3D1%2F3-1%2F4%5E%EF%BC%89)
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如果有理数a、b满足丨a-2丨+(1-b)²=0?试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2010)(b+2010)的值.(提示:1/2×3=1/2-1/3,1/3×4=1/3-1/4^)
如果有理数a、b满足丨a-2丨+(1-b)²=0?
试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2010)(b+2010)的值.(提示:1/2×3=1/2-1/3,1/3×4=1/3-1/4^)
如果有理数a、b满足丨a-2丨+(1-b)²=0?试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2010)(b+2010)的值.(提示:1/2×3=1/2-1/3,1/3×4=1/3-1/4^)
如果有理数a、b满足丨a-2丨+(1-b)²=0
则,a-2=0 1-b=0
a=2 b=1
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2010)(b+2010)
=1/2*1+1/3*2+1/3*4+/14*5+++++++.+1/2012*2011
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.-1/2011+1/2011-1/2012
=1-1/2012
=2011/2012
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