Question

高中数列题目,求证及求通项公式,详细过程.不要复制

Answer 1

n= an+1 - an

=(an-1 -an)/2

bn-1 = an - an-1

(bn-1)/bn=-2

所以 bn是公比为-0.5的等比数列

a1=1

a2-a1=1

a3-a2=-1/2

a4-a3=1/4

a5-a4=-1/8

.

an-an-1=(-1/2)^(n-2)

相加起来

an=1+1-1/2+1/4-1/8+...(-1/2)^(n-2)

=1+ (1-(-1/2)^(n-1))/(1-(-1/2))

=1+2(1-(-1/2)^(n-1))/3