已知{An}成等差数列,Bn=[A(n+1)]^2-An^2,求证数列{Bn}也成等差数列.回答的加悬赏、、
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已知{An}成等差数列,Bn=[A(n+1)]^2-An^2,求证数列{Bn}也成等差数列.回答的加悬赏、、已知{An}成等差数列,Bn=[A(n+1)]^2-An^2,求证数列{Bn}也成等差数列.
已知{An}成等差数列,Bn=[A(n+1)]^2-An^2,求证数列{Bn}也成等差数列.回答的加悬赏、、
已知{An}成等差数列,Bn=[A(n+1)]^2-An^2,求证数列{Bn}也成等差数列.
回答的加悬赏、、
已知{An}成等差数列,Bn=[A(n+1)]^2-An^2,求证数列{Bn}也成等差数列.回答的加悬赏、、
An=A1+(n-1)d
A(n+1)=A1+nd
Bn=(a1+nd)^2-[a1+(n-1)d]^2 =2nd^2+2da1-d^2
B(n-1)=[a1+(n-1)d]^2-[a1+(n-2)d]^2=2nd^2+2da1
Bn-B(n-1)=d^2
可得数列{Bn}是等 差数列
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