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Ariel asked in Science & MathematicsMathematics · 2 months ago

# 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.

Relevance
• rotchm
Lv 7
2 months ago

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.