This tag is for questions related to conditional convergence. A series or integral is said to be conditionally convergent if it converges, but it does not converge absolutely.
Questions tagged [conditional-convergence]
229 questions
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Does $a_n$ converge if $a_{n+1} = a_n + \frac{1}{e^{a_n}+1}$? Or does its convergence depend on $a_0$?
Does $a_n$ converge if$a_{n+1} = a_n + \frac{1}{e^{a_n}+1}$? Or does its convergence depend on $a_0$?
As described in the title, it seems intuitively that it should converge, but I don't know how to prove it.
n yk
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Conditionally Covergent Series
Looking to prove that the following series converges conditionally
$$\sum _{n=1}^{\infty}\frac{(-1)^{n+1}(1+n)^{\frac{1}{n}}}{n}$$
Plugging in some terms I see that,
$$\sum _{n=1}^{\infty}\frac{(-1)^{n+1}(1+n)^{\frac{1}{n}}}{n} = 2 -…
jh123
- 1,400
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Conditional convergence of $\int_1^{\infty} \frac{\sin(x)}{x}dx$?
What's a simple way to display $$\int_1^{\infty} \frac{\sin(x)}{x}dx$$ conditionally convergent (i.e. convergent, but not absolutely)?
mavavilj
- 7,270