Question

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

Answer 1

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

Answer 2

with Sigma n=1 to infinity

Answer 3

But that's a sum, not a sequence.

Answer 4

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

Answer 5

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

Answer 6

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.

Answer 7

oh okay. well if i wanted a sequence?

Answer 8

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.

Answer 9

thanks