Determine whether the following statements are true and give an explanation or counterexample.

a. Ifconverges, thenconverges.
b. If diverges, then diverges.

c. If ∑a_k converges, then ∑(a_k + 0.0001) also converges.

d. If ∑p^k diverges, then ∑(p + 0.001)^k diverges, for a fixed real number p.

e. If ∑k^-p converges, then ∑k^{-p + 0.001} converges.

f. Ifthen ∑a_k converges.

Transcribed Image Text:

Σο Οκ k=1 ак k=10 Σ