如果有理数a、b满足|ab-2|加(1-b)的2次方=0,试求:1/ab+1/(a+1)(b+1)+……+1/(a+2012)(b+2012)的值
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![如果有理数a、b满足|ab-2|加(1-b)的2次方=0,试求:1/ab+1/(a+1)(b+1)+……+1/(a+2012)(b+2012)的值](/uploads/image/z/9299871-63-1.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%7Cab-2%7C%E5%8A%A0%EF%BC%881-b%29%E7%9A%842%E6%AC%A1%E6%96%B9%3D0%2C%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%EF%BC%88a%2B2012%29%28b%2B2012%29%E7%9A%84%E5%80%BC)
如果有理数a、b满足|ab-2|加(1-b)的2次方=0,试求:1/ab+1/(a+1)(b+1)+……+1/(a+2012)(b+2012)的值
如果有理数a、b满足|ab-2|加(1-b)的2次方=0,试求:1/ab+1/(a+1)(b+1)+……+1/(a+2012)(b+2012)的值
如果有理数a、b满足|ab-2|加(1-b)的2次方=0,试求:1/ab+1/(a+1)(b+1)+……+1/(a+2012)(b+2012)的值
∵|ab-2|加(1-b)的2次方=0
故ab-2=0 1-b=0
a=2 b=1
∴1/ab+1/(a+1)(b+1)+……+1/(a+2012)(b+2012)的值
=1/2*1+1/3*2+1/4*3+.+1/2014*2013
=1-1/2+1/2-1/3+1/3-1/4+.+1/2013-1/2014
=1-1/2014
=2013/2014
|ab-2|加(1-b)的2次方=0
b=1
ab=2
a=2/b=2
1/ab+1/(a+1)(b+1)+……+1/(a+2012)(b+2012)
=1/1x2+1/2x3+...1/2013x2014
=1-1/2+1/2-1/3+...+1/2013-1/2014
=1-1/2014
=2013/2014
|ab-2|加(1-b)的2次方=0
即
|ab-2|=0,(1-b)的2次方=0
所以
ab=2,b=1
a=2,b=1
所以
1/ab+1/(a+1)(b+1)+……+1/(a+2012)(b+2012)
=1/1×2+1/2×3+。。。。+1/2013×2014
=1-1/2+1/2-1/3+。。。+1/2013-1/2014
=1-1/2014
=2013/2014