lim[1/4-1/8+1/16+……+(-1)^n-1 (1/2^n+1)]=
问题描述:
lim[1/4-1/8+1/16+……+(-1)^n-1 (1/2^n+1)]=
答
n→∞吗?
lim【n→∞】{1/4-1/8+1/16+……+[(-1)^(n-1)]{1/[2^(n+1)]}}
=lim【n→∞】{[(1/4)(1-(-1/2)^n]/(1+1/2)}
=lim【n→∞】{[1-(-1/2)^n]/6}
=1/6