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Hello guys so i started solving some problems for my class and i found this one, i really have no idea how to solve it can someone help me?

Find the real parameters a and b so $a_n$ and $b_n$ are both simultaneously convergent series

$a_n= a \sqrt{n+5}+b\sqrt{9n+5}-\sqrt{4n+3} $

$b_n= a \sqrt{9n+3}-b\sqrt{25n+30}+\sqrt{64n+15}$

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    You've said series, but you've written a sequence. Are you asking about convergence of $\sum a_n$ and $\sum b_n$, or of the sequences $(a_n)$ and $(b_n)$? – 2017-01-17
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    $\lim_{n\to\infty}a_n = (a+3b-2)\sqrt n$ and $\lim_{n\to\infty}b_n = (3a-5b+8)\sqrt n$, can you do it now? – 2017-01-17
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    Hi, yes i'm asking about the sequences $a_n$ and $b_n$ – 2017-01-17

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