MHB Need Support? Discover How to Get Help!

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Please help me
Thank you in advance
 
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This is my work
I am struggle at this point
 
\[ \lim_{k \to \infty} \left| \frac{[3(k+1)]!}{(k+1)(k+2)} \cdot \frac{k(k+1)}{(3k)!} \right| \]

\[ \lim_{k \to \infty} \left| \frac{k(3k+3)(3k+2)(3k+1)}{(k+2)}\right| \]

evaluate the limit ... what can you conclude?
 
Also, keep in mind it's a positive termed series, so the absolute values (while not incorrect) are unnecessary.
 

Thread 'About the definition of topological manifold using closed sets'

We all know the definition of n-dimensional topological manifold uses open sets and homeomorphisms onto the image as open set in ##\mathbb R^n##. It should be possible to reformulate the definition of n-dimensional topological manifold using closed sets on the manifold's topology and on ##\mathbb R^n## ? I'm positive for this. Perhaps the definition of smooth manifold would be problematic, though.
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