等差数列 (25 14:58:26)已知数列log2（an —1）为等差数列a1=3,a3=91.求an2.证明1/(a2-a1) +1/(a3-a2) +...+1/a(n+1)-an
问题描述：
等差数列 (25 14:58:26)
已知数列log2（an —1）为等差数列a1=3,a3=9
1.求an
2.证明1/(a2-a1) +1/(a3-a2) +...+1/a(n+1)-an
答
设公差为：dlog2(a1-1)=log2(2)=1log2(a3-1)-log2(a1-1)=2dd=[log2(8)-log2(2)]/2=1log2(an-1)=1+(n-1)*1=n2^n=an-1an=2^n+11/[a(n+1)-an]=1/{[2^(n+1)+1]-(2^n+1)}=1/{2^(n+1)-2^n}=1/(2^n)1/(a2-a1) +1/(a3-a2) +....