The ratio test will give you the answer: divergent.
If you do not know how to apply the ratio test, you should look it up because it is a standard and often (but not always) very useful method.
6/5/2020:
It is hard to write the ratio in this editor but I will try:
{3n+1/[3(n+1)(n+2)3]} * {3n(n+1)3/3n}
Inthe limit:
3n/[3(n+1)] goes to 1
[(n+1)/(n+2)]3 also goes to one
3n+1/3n leaves a 3 in the numerator
Thus the whole ratio goes to 3...which means the series diverges.
Fatima A.
Sir, I have tried and I got Lim n--> infinite for [(n+3)/ (n+1) ]^3 , so the answer is one , shall I stop here? Because when I do the three tests I get it is convegent, Lim n->infinite (1/(n+1)^3)=0 converges Decreasing and all terms all positive How it comes like divergent would please clarify
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06/04/20
Sava D.
tutor
Also, you need each term to go to zero, for the series to be convergent. Did you check that part?
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06/05/20
Fatima A.
Okay I will use thanks sir06/04/20