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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. 

Attachment image

1 Answer

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  • rotchm
    Lv 7
    2 months ago
    Favorite 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...

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