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converges for sure, and in fact i think the sum is not even 5

ignore the irrelavent -1 and +1 and use the root test, get it right away

It is hard to calculate using root test

not when the index is in the exponent, then it is easy

\[\sqrt[n]{2^n}=2\]!

What to do with +1 and -1?

Still have no idea how to do

if you want...you can use the comparison test

Compare with (2/3)^n?

sure...use the limit comparison test then.