Question

LIMIT FAST:

Answer 1

Find the limit
\[1+(-1)^n\]

Answer 2

As n approaches what?

Answer 3

limt n tends to what?

Answer 4

guess what: infinity

Answer 5

Oh, a Smart Alexander. Nice. Try to be more respetcful and cooperative.

What say you? Is "n" an integer? What does \((-1)^{n}\) do as n increases without bound?

Answer 6

Find the limit of the row :
\[x _{n}=1+(-1)^n\]

Answer 7

Much better. Using it as an index suggests that n is a Whole Number or Natural Number.

Okay, now answer the question.

What does \((−1)^{n}\) do as n increases without bound? How about as it takes on 1, 2, 3, and then 4? What does that piece do?

Answer 8

I'm not that stupid @tkhunny
\[(-1)^n=\left[\begin{matrix}-1 & if;n; isnot;even\\ 1 & if;n even\end{matrix}\right]\]

Answer 9

that (-1) provokes me an undetermination in the limit:
\[UNDETERMINATION:CASE:\left[ 1^{\infty } \right]\]

Answer 10

Who said you were stupid at all?

There you have it. The whole expression flops around between 2 and 0. Therefore, the individual terms do not converge

If we are talking about series, we can also say that there is no series convergence.