A quick to state puzzle:
If
$$S = 1 + \frac{1}{\sqrt[4]{2}} + \frac{1}{\sqrt[4]{3}} + \dots + \frac{1}{\sqrt[4]{10000}} $$
what is the integer part of $S$?
i.e. what is the integer part of
$$\sum_{k=1}^{10000} \frac{1}{k^{1/4}} $$
(integer part of $x$ = largest integer $\le x$)
[Solution]
If
$$S = 1 + \frac{1}{\sqrt[4]{2}} + \frac{1}{\sqrt[4]{3}} + \dots + \frac{1}{\sqrt[4]{10000}} $$
what is the integer part of $S$?
i.e. what is the integer part of
$$\sum_{k=1}^{10000} \frac{1}{k^{1/4}} $$
(integer part of $x$ = largest integer $\le x$)
[Solution]
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