若等差数列

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证明：设等差数列{an}的公差为d左边=[(√a2-√a1)/(a2-a1)]+[(√a3-√a2)/(a3-a2)]+...+[(√an-√an_1)/(an-an_1)]=[(√an-√a1)/d]=(an-a1)/[(√an+√a1)d]=[(n-1)d]/[(√an+√a1)d]=(n-1)/(√an+√a1)=右边证毕