Question

why does 1/x diverge while 1/x^2 converge and does 1/x^3 converge too?

Answer 1

Because x^-1 always makes an unfriendly number. Anything like x^-a where a > 1 will make friendly numbers which always converge.

Answer 2

Do you know about p series? If you have a series of 1/(x^p), it is a p-series. Basically in a p-series, if p is greater than one, it converges, and if p is less than or equal to one, it diverges.

Answer 3

thanks john i just wasnt quite sure. do u guys know the difference between a geometric and harmonic series? how do you id them thnks

Answer 4

In a geometric series, \[\sum_{n=1}^{infty} 1/n\]
Is a harmonic series, while
\[\sum_{n=0}^{\infty} a1 * r^n \]
Is a geometric series.

A harmonic series is just a series with an increasing denominator with each term. A geometric series has a constant ratio between each term, r.