Prove the following by the principle of mathematical induction: \[ \frac{1}{25}+\frac{1}{5.8}+\f...

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Prove the following by the principle of mathematical induction:
\[
\frac{1}{25}+\frac{1}{5.8}+\frac{1}{8.11}+\ldots+\frac{1}{(3 n-1)(3 n+2)}=\frac{n}{6 n+4}
\]
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