Question 361872
The given series can be obtained by deleting infinitely many number of terms from the p-series {{{1+1/2^p + 1/3^p+ 1/4^p }}}+...+{{{1/n^p}}}+..., with p = 2.  In such case the p-series is absolutely convergent.  Since the given series is just {{{1+1/4^2 + 1/7^2 + 1/10^2 }}}+...+{{{1/n^2}}}+..., the series is also absolutely convergent, and consequently convergent.