Do the sequences converge or diverge?

3+e^(-2n)

i know it diverges but how do i show out my work please:)

Question

Do the sequences converge or diverge? 

3+e^(-2n) 

i know it diverges but how do i show out my work please:)

anonymous · Answer

i think it converges to 3, as $n\to \infty$ you have $e^{-2n}=\frac{1}{e^{2n}}\to 0$

megannicole51 · Answer

i put it in wolfram and it says it does not converge so idkk lol

anonymous · Answer

sequence right? not a sum

agent0smith · Answer

The *terms* do converge to 3, the sum doesn't, since you're adding 3 endlessly.

anonymous · Answer

The sequence can be rewritten as 3 + e/(2^n).
As n gets very large (approaches infinity), e/2^n is e/a very large number, so e/large number approaches 0,
so the entire sequence approaches 3 + 0 = 3. It converges.

anonymous · Answer

show the wolfram link, maybe i am wrong but i don't think so
the sum does not converge, but this says "sequence"

megannicole51 · Answer

oooh lol smart man @satellite73 ....i put it in a series not a sequence!

anonymous · Answer

guessed it right!

megannicole51 · Answer

okay awesome thank you:)