Question

Find if the sequence an = 5/(n+2) diverges or converges.

I think it diverges because the limit as x approaches infinity does not exist.

Answer 1

you know that 1/n diverges
so, also does 1/(n+2) since

∞
∑ 1/(n+2)
n=1

is the same as

∞
∑ 1/n
n=3

lopping off the first two terms and multiplying by 5 doesn't affect the divergence