# 微積分收斂發散的問題~會的人請幫幫忙

Decide whether the given statement is true or false. If it is true, prove.
If it is false, give a counterexample.
(a). If lim (n→∞)An = 0, then Σ(n=1~∞) An converges.
(b). If Σ(n=1~∞) An and Σ(n=1~∞) Bn both diverge, then
Σ(n=1~∞) (An+Bn) ...
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Decide whether the given statement is true or false. If it is true, prove.

If it is false, give a counterexample.

(a). If lim (n→∞)An = 0, then Σ(n=1~∞) An converges.

(b). If Σ(n=1~∞) An and Σ(n=1~∞) Bn both diverge, then

Σ(n=1~∞) (An+Bn) also diverges.

(c). If { An } is a increasing sequence, then lim(n→∞) An= ∞

(d)Σ(n=1~∞) (1+1/n)^n diverges.

If it is false, give a counterexample.

(a). If lim (n→∞)An = 0, then Σ(n=1~∞) An converges.

(b). If Σ(n=1~∞) An and Σ(n=1~∞) Bn both diverge, then

Σ(n=1~∞) (An+Bn) also diverges.

(c). If { An } is a increasing sequence, then lim(n→∞) An= ∞

(d)Σ(n=1~∞) (1+1/n)^n diverges.

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