Ininfite series and Analysis. Suppose Ak> 0 k a natural number, and Bk = 1/k[A1+A2+...+Ak) Show Σ Bk is conve?
Suppose Ak> 0 k a natural number, and Bk = 1/k[A1+A2+...+Ak] Show Σ Bk is convergent.
Update:Yes, you are right. It should be shown that Σ Bk is divergent but how?
Update 3:Nevermind, your explanation was on pair with my thinking, thanks!
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Um, Σ B(k) is NEVER convergent.
B dominates the sequence C defined by C(k) = A(1)/k,
and Σ C(k) is then A(1) times the harmonic series which
is of course divergent, so Σ B(k) is divergent as well.
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What are the terms A1, A2, etc????????