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　次の数列$a_1, \, a_2, \, \cdots\cdots, \, a_n, \, \cdots\cdots$の収束，発散を調べ，
解答欄の表に番号を記入せよ．
またその理由を述べよ．
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\item[(1)]$\displaystyle a_n=\frac{1}{n}\sin n$
\item[(2)]$\displaystyle a_n=n^2\sin\frac{1}{n}$
\item[(3)]$\displaystyle a_n=n\cos\frac{n\pi}{4}$
\item[(4)]$a_n=\sqrt{2n}-n$
\item[(5)]$\displaystyle a_n=\frac{1}{n^2}+\frac{1}{{(n+1)}^2}+\cdots\cdots+\frac{1}{{(2n)}^2}$
\item[(6)]$\displaystyle a_n=\frac{1}{n}+\frac{1}{n+1}+\cdots\cdots+\frac{1}{2n}$
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