已知数列{an}的前n项和Sn=2^n减1(n属于N)则limn到无穷乘an+2/Sn=?急答案为1/2

Question

已知数列{an}的前n项和Sn=2^n减1(n属于N)则lim n到无穷乘an+2/Sn=?急答案为1/2

Answer 1

Sn=2ⁿ-1,
=> an=2^(n-1),
=> lim(an+2)/Sn
=lim[2^(n-1)+2]/(2ⁿ-1)
=lim[(2ⁿ-1)/2+5/2]/(2ⁿ-1)
=lim[1/2+5/2/(2ⁿ-1)]
n->∞时, (2ⁿ-1)->∞, 1/(2ⁿ-1)->0
则limlim(an+2)/Sn=1/2+0=1/2
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