could I please get help with the following true/false questions? I have been trying to use the theorems in my textbook, but just don't feel too sure on where I'm at...
(infinity upper bound, k=1 on the bottom)If ∑ak converges, then when k=10 it also converges. I said TRUE.
(infinity upper bound, k=1 on the bottom)If ∑ak diverges, then when k=10 it also diverges. I said TRUE.
If just ∑ak converges, then ∑(ak+.00001) also converges (I'm not sure)
If ∑p^k diverges, then ∑(p+.001)^k diverges, for a fixed real number p. True? (not sure)
If ∑k^-p converges, then ∑k^(-p+.001) converges. Again I feel like this is TRUE.
If limit as k approaches infinity ak=0, then ∑ak converges. True (I feel fairly confident on this one)
Thank you to all who respond!!