设bn=(1/2)的n次方,sn=1+b1+b2+.+bn,求sn
问题描述:
设bn=(1/2)的n次方,sn=1+b1+b2+.+bn,求sn
答
设bn=(1/2)的n次方,sn=1+b1+b2+.+bn,求sn
利用等比数列求和公式:
sn=1+b1+b2+.+bn
=1+1/2+1/4+1/8 +……+1/2^n]
= (1-1/2^(n+1))/(1-1/2)
=2-1/2^n.