※ 引述《Dirichlet ( )》之銘言:
: ※ 引述《plover (>//////<)》之銘言:
: : Show that the convergence of Σ a_n, where a_n > 0 for all n
: : implies the convergence of Σ{(a_n)^(1/2)}/n.
: [(a_n)^(1/2) - 1/n]^2 = a_n + 1/n^2 - 2[(a_n)^(1/2)]/n ≧ 0
: a_n + 1/n^2 ≧ 2[(a_n)^(1/2)]/n
: By assumption, the fact Σ1/n^2 conv. and Comparison test
: we know Σ{(a_n)^(1/2)}/n conv.
如果題目「Σ{(a_n)^(1/2)}/n」改成「Σ{(a_n)^(1/2)} n^{-p} for real p」,
那麼 Σ{(a_n)^(1/2)} n^{-p} 的斂散性又是如何?
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.218.142