Question

Suppose that \(\lim \sup a_{n} = c, c>0\) Prove that \(\lim \sup (a^{2}_{n}) = c^{2}\)

Answer 1

this may not be formal but this is what im thinking :

\[\large \limsup (a_n^2) = e^{2\limsup (\ln a_n)} =e^{2\ln c } =c^2\]

Answer 2

Thats pretty interesting. But yeah, we basically cannot use any sort of idea that hasn't been covered in class yet. So no ln, sin, cos, differentiation, integration, etc. We've had students in our class try to use ln and cosine specifically in our questions before and yeah, no go.

Answer 3

Can you draw that?

Answer 4

I wouldnt really know how to give a visual representation, no.

Answer 5

what is sup?

Answer 6

limit superior......

Answer 7

Never heard of that. What math is this?

Answer 8

Real analysis.

Answer 9

hmm.. grade?

Answer 10

Its a 4th year math class.

Answer 11

not true

Answer 12

you need to add a condition to your problem to make it true

Answer 13

Hmm... well, this is exactly how the problem is asked:



No other information is given. What condition is missing?