Question

See if the following sequence converges or diverges?

Answer 1

seems unlikely

Answer 2

I was thinking of squaring it, but it seems illegal

Answer 3

think of it as \(a_n=n-n^2\)

Answer 4

converge to 1?

Answer 5

oh no goes to \(-\infty\)

Answer 6

the second term is basically the square of the first

Answer 7

how would we show this though

Answer 8

what can you use?

Answer 9

I was thinking of squaring both sides first?

Answer 10

Are we able to do this?

Answer 11

oh no you can't do that !

Answer 12

plus it would be a huge mess

Answer 13

you could multiply top and bottom by the conjugate i guess

Answer 14

there is no top or bottom?

Answer 15

\[\frac{n-(n^2-1)}{\sqrt{n}+\sqrt{n^2+1}}\]

Answer 16

it is that imaginary one in the denominator

Answer 17

okay.... so then we say all of that is equal to infinity?

Answer 18

minus infinity