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]

198 questions

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### What does this series do: $\ln((2n+1)/(2n-1))$? (Converges or Diverges?)

what this series do when n is going to be a large number.
ln((2n+1)/(2n-1)) when n is tending to infinity?
I used integral test, ratio test, comparison test and ...
what do you think about this series ???

**-1**

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**1**answer

### 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

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**-2**

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**2**answers

### Infinite series convergence question

$$\sum_{n=3}^{\infty}\frac{(-1)^n}{\log n}$$
Can the conditional convergence of this series be proved by alternating series test, since you need n to be a natural number for the alternating series test and here we have n is a natural number from 3…

user504498

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