Recent content by Sun God

Thanks for the prompt response! Okay, so to try to simplify it/put it in more understandable phrasing (for my own sake): for a sequence to be proven divergent, I just have to show that for any x there is an open neighborhood of x such that the sequence does not have infinitely many terms...

I feel like I'm missing something obvious, but anyway, in the text it states: lim as n→∞ of an+bn = ( lim as n→∞ of an ) + ( lim as n→∞ of bn ) But say an is 1/n and bn is n. Then the limit of the sum is n/n = 1, but the lim as n→∞ of bn doesn't exist and this property doesn't work...

Ahaha... no wonder it wasn't making sense to me. It's clearer now, much thanks for your patience! (To clarify for myself and maybe others: it was a matter of finding nonzero coefficients a, b, c and still have the linear combination of the functions equal to zero; if we found such a, b, and...

Okay, to follow the above poster: I have a system of equations of a + bln2 = 0 b + 2c = 0 I set c = 1 and b = -2 Then I get a = 2ln2 Plug this back into the original equation to get 2ln2 - 2ln2 - 2lnx + 2lnx = 0 Which is always true, therefore the functions ARE linearly...

Thank you for the help. Apologies again if I'm missing something that's obvious, but I still cannot find the answer. This is my process: a(1) + b(ln2x) + c(ln(x^2)) = a(1) + b(ln2 + lnx) + c(2lnx) = a + bln2 + blnx + 2clnx = a + b*ln2 + (b+2c)*lnx After trying to play around with it some...

Homework Statement Test the set of {1, ln(2x), ln(x^2)} for linear independence in F, the set of all functions. If it is linearly dependent, express one of the functions as a linear combination of the others. Homework Equations N/A The Attempt at a Solution I know if [ a(1)...

For instance: 1/(e^.5t) + 1/(e^-7t) As t grows larger, the left term goes to 0, but the right term goes to infinity. Would I be correct in saying that the limit of the sum is infinity because the (absolute value of the) coefficient of t in the term that tends to infinity is larger than...