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Test the series below for convergence using the root test.

`sum_(n=1)^oo ((7 n^2)/(5 n + 3))^n`

The limit of the root test simplifies to `lim_(n rarr oo) |f(n)|` where

`f(n)=`   .

The limit is   .
(enter oo for infinity if needed)

Based on this, the series .

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