Question

已知數(shù)列{log₂(a_n-1)}(n∈N^*)為等差數(shù)列,且a₁=3,a₃=5,則(++…+)等于(    )

A.2                 B.               C.1                D.

Answer 1

解析：令b_n=log₂(a_n-1),則{b_n}成等差數(shù)列,b₁=log₂2=1,b₂=log₂4=2,則b_n=n=log₂(a_n-1),

∴a_n=2ⁿ+1,

a_n+1-a_n=2ⁿ⁺¹+1-(2ⁿ+1)=2ⁿ.

∴原式=(++…+)=1.

答案：C