Hello All: I have been having a hard time with some homework problems, 5/20 can't be done by me, so I was hoping y'all could help! (Part II)

#3) Sum (n=1 to Infinity) of tan(1/n)

Divergence Test doesn't work (lim = 0), so I'm at a loss. Can I use integral test? Is this even a decreasing function? I'm terrible with trig related identities

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This is a positive series and thus we can use the limit test, and as , the series diverges. #4) Sum (n=1 to Infinity) of (n!)^n/(n^4n) Part of me wants to use ratio test, but would that be n+1!^(n+1) etc. or just n!^(n+1) or neither. Or, I could separate and use root test, but again not sure of the validity of doing that.