数列{an}中,若a1=a2=1,且an+2=an+1+an(n∈N^2),用数学归纳法证明:a5n能被5整除

问题描述:

数列{an}中,若a1=a2=1,且an+2=an+1+an(n∈N^2),用数学归纳法证明:a5n能被5整除

当n=1时 a3=a1+a2=2 a4=a3+a2=3 a5=a3+a4=5 满足假设n=k满足 a(5k+5)=a(5k+4)+a(5k+3) = 2a(5k+3)+a(5k+2)=2[a(5k+2)+a(5k+1)]+a(5k+1)+a(5k)=2[a(5k+1)+a(5k)+a(5k+1)]+a(5k+1)+a(5k)=5a(5k+1)+3a(5k)5a(5k+1)能被5...