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 '2-sphere intrinsic definition by gluing disks' boundaries'

A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.
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