How would you write the following sequence 1/2 , 1/(2^2) , 1/3, 1/(3^2) etc

Question

hero · Answer

What do you mean "How do you write it?" Looks like you already wrote it...

anonymous · Answer

with Sigma n=1 to infinity

anonymous · Answer

But that's a sum, not a sequence.

anonymous · Answer

$$\sum_{n=2}^{\infty}\left(\frac{1}{n}+\frac{1}{n^2}\right)$$

anonymous · Answer

If you put n=2 for the first term that gives you 3/4, not 1/2

anonymous · Answer

I know, but you said that you wanted to use SIGMA, so it's irrelevant. However, if what you're looking for is a SEQUENCE, then my answer is not correct.

anonymous · Answer

oh okay. well if i wanted a sequence?

anonymous · Answer

I'd write it as a juxtaposition of disjoint sequences, as follows:$$\left(\frac{1}{n}\right)_{2n\in\mathbb{N}}\left(\frac{1}{n^2}\right)_{(2n+1)\in\mathbb{N}}.$$But I don't know if that's okay with you.

anonymous · Answer

thanks