Question

Guys, just a quick question.
When finding convergence/divergence of a series let's say sigma (ca_n) where c is any constant. Can I pull out the c out of sigma notation without knowing if the series converges or diverges? for example sigma(ca_n) as c*sigma(a_n) without knowing if a_n converges or not.

Answer 1

i believe you can....im trying really really hard to think of counter examples, but none are coming up. as long as the constant isnt 0, you should be good.\[c\neq 0\Longrightarrow \sum ca_n=c\sum a_n\]

Answer 2

Then you can worry about finding out if \[\sum a_n\]converges or not.

Answer 3

Thank you very much my friend

Answer 4

Yes, by the Monotone Convergence Theorem and the sum properties of sequences.