Asked by Anonymous
I'm asked to find the limit as n approaches infinity of : [(2^(n) +1]/ [2^(n+1)]. The review we were given has [1+ 2^(-n)] / 2 as the next step, but I'm not quite sure how to make that leap myself. The final answer is 1/2. How do you solve this limit?
Answers
Answered by
Steve
I'd go with this:
(2^n+1)/2^(n+1)
= 2^n/2^(n+1) + 1/2^(n+1)
= 1/2 + 1/2^(n+1)
-> 1/2 as n->∞
The suggestion requires you to multiply top and bottom by 2^-n.
(2^n+1)/2^(n+1)
= 2^n/2^(n+1) + 1/2^(n+1)
= 1/2 + 1/2^(n+1)
-> 1/2 as n->∞
The suggestion requires you to multiply top and bottom by 2^-n.
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