Question

已知数列{An} {Bn}满足A1=B1=1 An+1-An=Bn+1/Bn 求下列数列的前n项和 (1){Ban} (2) {An/Bn}

Answer 1

a1+a1=1
a1=1/2
an+Sn=n
a(n-1)+S(n-1)=n-1
2式相减
an-a(n-1)+an=1
2an=a(n-1)+1
an-1=1/2[a(n-1)-1]
所以an-1=1/2*1/2^(n-1)
an=1/2^n+1
bn+1=an+1-an=1/2^n+1-1/2^(n-1)-1=-1/2^n
所以bn
是等比数列