# lim_(n->oo)(1+1/n)^n = # ?
It is obvious that:
Using Bernoulli's inequality again:
Using inequality of arithmetic and geometric means:
it follows:
Finally,
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Thus, we undo the natural logarithm to get:
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so
Finally
and
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The limit of ( (1 + \frac{1}{n})^n ) as ( n ) approaches infinity is equal to ( e ), where ( e ) is Euler's number, approximately ( 2.71828 ).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- How do you find the nth partial sum, determine whether the series converges and find the sum when it exists given #1+1/3+1/9+...+(1/3)^n+...#?
- Integrate the following using infinite #\bb\text(series)# ?
- How do you use the Alternating Series Test?
- What is the Alternating Series Test of convergence?
- Is the sequence divergent or convergent?

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