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Could someone help me with this limit problem? ?
I am not sure how the answer is obtained. I do know that the
limit (as n->infinity) of (1+ (1/n))^n is e^x
but I am finding it difficult to manipulate the answer with this information.
1 Answer
- rotchmLv 71 month agoFavorite Answer
First, "n->infinity of (1+ (1/n))^n is e^x ". NO it is not.
n->infinity of (1+ (1/n))^n is e.
Let's ignore the t since it really has nothing to do with it.
(1+r/n)^n = (1+1/(n/r))^n = [(1+1/(n/r))^(n/r)]^r.
Look at the expression in brackets. Its simply e.
(Indeed, doing the change of var n/r = u you
get (1+1/u)^u which gives e in the limit.)
So, [(1+1/(n/r))^(n/r)]^r. = e^r.
^t each side answers your original question.
I've answered you in the past and I was the first to answer and I had the good answers yet you voted other people who made mistakes. That was very dishonest of you to do so. I do hope you will be honest and grateful this time...
