Question

What is the difference between divergence and convergence?

Answer 1

I can give you an example to explain if necessary

Answer 2

divergence goes off into infinity; and convergence settles down to something that we can define

Answer 3

determining "d" or "c" can be a pain tho

Answer 4

wait just gotta show u something

Answer 5

\[\int\limits_{1}^{\infty}1/x ^{2}\]

Answer 6

convergent I believe; since it gets real small real quick

Answer 7

and lets say \[\int\limits_{1}^{\infty}1/\sqrt{x}\]

Answer 8

x^(-1/2) gets big

Answer 9

i think i got that right lol

Answer 10

ya u did lol

Answer 11

but they are both getting smaller

Answer 12

1/x is a dividing line; 1/x diverges, but anything just shy of it bigger, like x^(-1.00000000001) converges

Answer 13

the sqrt doesnt do it fast enough

Answer 14

1/x goes to gets smaller buth the sums never settle down

Answer 15

oh ok

Answer 16

the convergence is called a least upper boundary, not that that makes much difference. It just says that we can add up the partial sums and they tend towards a nice number or they dont

Answer 17

oh ok get it now thanks :D

Answer 18

youre welcome :)

Answer 19

\[\int_a^{\infty} \frac{1}{x^r}dx=\int_a^{\infty}x^{-r}dx\] converges if
\[r>1\] diverges if
\[r\leq 1\]