Xn=(1+1/2∧2)(1+1/2∧4).(1+1/2∧(2∧n))求极限limXnn趋近于无穷

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Xn=(1+1/2∧2)(1+1/2∧4).(1+1/2∧(2∧n))求极限limXnn趋近于无穷
Xn=(1+1/2∧2)(1+1/2∧4).(1+1/2∧(2∧n))求极限limXn
n趋近于无穷

Xn=(1+1/2∧2)(1+1/2∧4).(1+1/2∧(2∧n))求极限limXnn趋近于无穷
(1-1/2^2)Xn=(1-1/2^2)(1+1/2^2)(1+1/2^4).(1+1/2^(2^n))
=(1-1/2^4)(1+1/2^4).(1+1/2^(2^n))
=...
=1-1/2^(2^(2n))
令n->无穷,右端=1-0=1
左端=(3/4)lim n->∞ Xn
所以
lim n->∞ Xn=4/3