# What is limit 1/(1-5^(1/x)) as x approaches to positive infinity ?

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Let's try a couple of values for

We can observe two facts:

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Figure out the direction/limit of the variable-controlled part first, then the rest falls into place.

Playing with a few numbers will quickly demonstrate that the term:

The denominator difference

Thus, the "limit" of the expression will be:

It is actually almost a straight line with a slope of

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