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 'Apparent counter-example to Cauchy-Goursat theorem (Complex Analysis)'

I posted this question on math-stackexchange but apparently I asked something stupid and I was downvoted. I still don't have an answer to my question so I hope someone in here can help me or at least explain me why I am asking something stupid. I started studying Complex Analysis and came upon the following theorem which is a direct consequence of the Cauchy-Goursat theorem: Let ##f:D\to\mathbb{C}## be an anlytic function over a simply connected region ##D##. If ##a## and ##z## are part of...
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