# What is the sum of the infinite geometric series #sum_(n=1)^oo2^n/5^(n-1)# ?

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The sum of the infinite geometric series ( \sum_{n=1}^{\infty} \frac{2^n}{5^{n-1}} ) can be calculated using the formula for the sum of an infinite geometric series, which is ( \frac{a}{1 - r} ), where ( a ) is the first term and ( r ) is the common ratio. In this series, the first term ( a ) is ( \frac{2}{5} ) and the common ratio ( r ) is ( \frac{2}{5} ). Therefore,

[ \sum_{n=1}^{\infty} \frac{2^n}{5^{n-1}} = \frac{\frac{2}{5}}{1 - \frac{2}{5}} ]

[ = \frac{\frac{2}{5}}{\frac{3}{5}} ]

[ = \frac{2}{3} ]

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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.

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