An=n+1,Bn=tan(An)*tan(An+1),求Bn的前n项和

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An=n+1,Bn=tan(An)*tan(An+1),求Bn的前n项和

An=n+1,Bn=tan(An)*tan(An+1),求Bn的前n项和
An=n+1,Bn=tan(An)*tan(An+1),求Bn的前n项和

An=n+1,Bn=tan(An)*tan(An+1),求Bn的前n项和
tan[n+2-(n+1)]=tan(1)={tan(n+2)-tan(n+1)}/[1+tan(n+2)tan(n+1)],
tan(n+2)tan(n+1)=b(n)={tan(n+2)-tan(n+1)}/tan(1) - 1
b(1)+b(2)+...+b(n)=[1/tan(1)]{tan(3)-tan(2) + tan(4)-tan(3)+...+tan(n+1)-tan(n) + tan(n+2)-tan(n+1)} - n
=[1/tan(1)]{tan(n+2)-tan(2)} - n
=[tan(n+2)-tan(2)]/tan(1) - n

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