[微積] 級數收斂
∞ k
Σ ------- converge or diverge?
k=0 k^2+3
這題我有兩個想法
1.積分測試
做 x
------- 的瑕積分 若收斂 則級數收斂
x^2+3
這個我已經算完了 答案是發散的
2.發散定理
k
let a_k = ------
k^2+3
k 1
lim a_k = lim -------- = ---- =0
k->∞ k->∞ k^2+3 ∞
但發散定理告訴我 若 lim a_k = 0
k->∞
則 此級數收斂
跟第一種想法結果矛盾@@ 怎麼會這樣呢??
還是發散定理在使用上有什麼限制呢??
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