If we have a series of numbers $$1^5 + 2^5 + 3^5 + \cdots + (10^n)^5.$$ Final sum of the series is approximately equal $16666\ldots$ .
If there is more and more numbers in the series is the result of closer and closer to $16666\ldots$ .
For example if the last number $1000$ or $10000$ or $100000$ and so on, the final sum is closer to $16666\ldots$ . If it is true (of course it is), can we conclude that $$1^5 + 2^5 + 3^5 + \cdots = \frac 1 6$$
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