Recent questions tagged convergence

0 votes
1 answer
1
3 votes
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4
1 votes
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8
Let $a_{n}=(n+1)^{100} e^{-\sqrt{n}}$ for $n \geq 1$. Then the sequence $(a_{n})_{n}$ isUnboundedBounded but does not converge Bounded and converges to $1$Bounded and con...
1 votes
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9
Suppose $f_{n}(x)$ is a sequence of continuous functions on the closed interval $[0, 1]$ converging to $0$ point wise. Then the integral $\int_{0}^{1} f_{n}(x) \text{d}x...
1 votes
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10
The series$\sum_{n=1}^{\infty}\frac{\sqrt{n+1}-\sqrt{n}}{n}$diverges.
1 votes
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11
1 votes
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12
2 votes
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14
Define $\left \{ x_{n} \right \}$ as $x_{1}=0.1,x_{2}=0.101,x_{3}=0.101001,\dots$ Then the sequence $\left \{ x_{n} \right \}$.Converges to a rational numberConverges to ...
2 votes
1 answer
16
2 votes
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17
The series $$\sum ^{\infty }_{n=1}\frac{(-1)^{n+1}}{\sqrt{n}}$$ Converges but not absolutely. Converges absolutely. Diverges. None of the above.
1 votes
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18
The radius of convergence of the power series$$\sum_{}^{\infty} \frac{(3m)!}{(m!)^3}x^{3m}$$ is: _____________
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