已知/ab-2/与/b-1/互为相反数,试求代数式 1 1 1 1 —+ ---------- + ---------- + .+ --------------1 1 1 1—+ ---------- + ---------- + ......+ ----------------的值ab (a+1)(b+1) (a+2)(b+2) (a+2009)(b+2009)
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![已知/ab-2/与/b-1/互为相反数,试求代数式 1 1 1 1 —+ ---------- + ---------- + .+ --------------1 1 1 1—+ ---------- + ---------- + ......+ ----------------的值ab (a+1)(b+1) (a+2)(b+2) (a+2009)(b+2009)](/uploads/image/z/7133119-7-9.jpg?t=%E5%B7%B2%E7%9F%A5%2Fab-2%2F%E4%B8%8E%2Fb-1%2F%E4%BA%92%E4%B8%BA%E7%9B%B8%E5%8F%8D%E6%95%B0%2C%E8%AF%95%E6%B1%82%E4%BB%A3%E6%95%B0%E5%BC%8F+1+1+1+1+%E2%80%94%2B+----------+%2B+----------+%2B+.%2B+--------------1+1+1+1%E2%80%94%2B+----------+%2B+----------+%2B+......%2B+----------------%E7%9A%84%E5%80%BCab+%28a%2B1%29%28b%2B1%29+%28a%2B2%29%28b%2B2%29+%28a%2B2009%29%28b%2B2009%29)
已知/ab-2/与/b-1/互为相反数,试求代数式 1 1 1 1 —+ ---------- + ---------- + .+ --------------1 1 1 1—+ ---------- + ---------- + ......+ ----------------的值ab (a+1)(b+1) (a+2)(b+2) (a+2009)(b+2009)
已知/ab-2/与/b-1/互为相反数,试求代数式 1 1 1 1 —+ ---------- + ---------- + .+ --------------
1 1 1 1
—+ ---------- + ---------- + ......+ ----------------的值
ab (a+1)(b+1) (a+2)(b+2) (a+2009)(b+2009)
已知/ab-2/与/b-1/互为相反数,试求代数式 1 1 1 1 —+ ---------- + ---------- + .+ --------------1 1 1 1—+ ---------- + ---------- + ......+ ----------------的值ab (a+1)(b+1) (a+2)(b+2) (a+2009)(b+2009)
/ab-2/与/b-1/互为相反数,则必都为0,则b=1,a=2
1/1*2+1/2*3+1/3*4+.+1/2010*2011=
1-1/2+1/2-1/3+1/3-1/4+1/2010-1/2011=1-1/2011=2010/2011
两绝对值互为相反数,则这两个数皆为0,
b-1=0 b=1
ab-2=0 ab=2 a=2
原式=1/2+1/(2*3)+1/(3*4)+...+1/(2010*2011)
=1/2+(1/2-1/3)+(1/3-1/4)+...+1/2010-1/2011
=1-1/2011
=2010/2011
/ab-2/与/b-1/互为相反数
∴ab=2,b=1
∴a=2,b=1
原式=1/1-1/2+1/2-1/3+1/3-1/4+……+1/2010-1/2011
=1-1/2011
=2010/2011
/ab-2/与/b-1/互为相反数
∴ab=2,b=1
∴a=2,b=1
原式=1/1-1/2+1/2-1/3+1/3-1/4+……+1/2010-1/2011
=1-1/2011
=2010/2011