已知:字母a、b满足√(a-1)+√(b-2)=0,求:1/(ab)+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2011)(b+2011)的值
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![已知:字母a、b满足√(a-1)+√(b-2)=0,求:1/(ab)+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2011)(b+2011)的值](/uploads/image/z/13941204-60-4.jpg?t=%E5%B7%B2%E7%9F%A5%EF%BC%9A%E5%AD%97%E6%AF%8Da%E3%80%81b%E6%BB%A1%E8%B6%B3%E2%88%9A%EF%BC%88a-1%EF%BC%89%2B%E2%88%9A%EF%BC%88b-2%EF%BC%89%3D0%2C%E6%B1%82%EF%BC%9A1%2F%EF%BC%88ab%EF%BC%89%2B1%2F%EF%BC%88a%2B1%EF%BC%89%EF%BC%88b%2B1%EF%BC%89%2B1%2F%EF%BC%88a%2B2%EF%BC%89%EF%BC%88b%2B2%EF%BC%89%2B%E2%80%A6%E2%80%A6%2B1%2F%EF%BC%88a%2B2011%EF%BC%89%EF%BC%88b%2B2011%EF%BC%89%E7%9A%84%E5%80%BC)
已知:字母a、b满足√(a-1)+√(b-2)=0,求:1/(ab)+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2011)(b+2011)的值
已知:字母a、b满足√(a-1)+√(b-2)=0,求:
1/(ab)+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2011)(b+2011)的值
已知:字母a、b满足√(a-1)+√(b-2)=0,求:1/(ab)+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2011)(b+2011)的值
∵√(a-1)+√(b-2)=0
∴a-1=0
b-2=0
∴a=1
b=2
1/(ab)+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2011)(b+2011)
=1/1×2+1/2×3+1/3×4+1/4×5+……+1/2012×2013
=1-1/2+1/2-1/3+1/3-1/4+……+1/2012-1/2013
=1-1/2013
=2012/2013
√(a-1)+√(b-2)=0
a-1=0 ,b-2=0
解得 a=1 ,b=2
1/(ab)+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2011)(b+2011)
=1/(1×2) +1/(2×3) +1/(3×4)+...+1/(2012×2013)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/20...
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√(a-1)+√(b-2)=0
a-1=0 ,b-2=0
解得 a=1 ,b=2
1/(ab)+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2011)(b+2011)
=1/(1×2) +1/(2×3) +1/(3×4)+...+1/(2012×2013)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/2012-1/2013
=1-1/2013
=2012/2013
中间部分一正一负都一一消去.
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∵字母a、b满足√(a-1)+√(b-2)=0
∴a-1=0, b-2=0
即a=1, b=2
1/(ab)+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2011)(b+2011)
=1/1x2+1/2x3+1/3x4+……+1/2012x2013
=1-1/2+1/2-1/3+1/3-1/4+……+1/2012-1/2013
=1-1/2013
=2012/2013