已知数列{An},{Dn}满足A1=B1=1,An+1-An=Bn+1/Bn=2,N∈ N*,则数列{Ban}的前10项和为?
问题描述:
已知数列{An},{Dn}满足A1=B1=1,An+1-An=Bn+1/Bn=2,N∈ N*,则数列{Ban}的前10项和为?
答
An:1,3,5,7,9,...
Bn:2,4,8,16,32,...
Ban:B1, B3, B5, B7,...,B19,即2,8,32,...,2^19.
B1+B3+B5+...+B19=(2-2*2^19)/(1-2)=2^20-2.即为所求.