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### Zero divided by infinite

The result of the division

is no surprise.

##### Explanation

The numerator of the fraction is zero, and the denominator is unequal zero. But it also applies to

and now you can expect that every real number *x* gives

However, take care, as infinity is not a number, and so

is undefined. If this division emerges in another way, you will get a solution, as

Here you work with *n*→∞ and that means: It approaches infinite, but is not infinite. The nominator and the denominator get the the same (infinite) value, and a division is thus allowed.