Question

converge or diverge? If the sequence does converge, what number do the terms of the sequence converge to?

Answer 1

The sequence does not converge.
The sequence converges to 100.
The sequence converges to -100.
The sequence converges to zero.

Answer 2

cool name

Answer 3

@Michele_Laino

Answer 4

What's the value of
\[\lim_{n\to\infty}(-1)^n\frac{100n}{100+n}\,?\]

Answer 5

100n

Answer 6

No, you can find the limit by comparing the coefficients of the \(n\) terms in the numerator and denominator.

Meanwhile, \(\lim_{n\to\infty}(-1)^n=\pm1\).
\[\lim_{n\to\infty}(-1)^n\frac{100n}{100+n}=\left(\lim_{n\to\infty}(-1)^n\right)\left(\lim_{n\to\infty}\frac{100n}{100+n}\right)=\pm\lim_{n\to\infty}\frac{100n}{100+n}\]

Answer 7

so you think its B

Answer 8

Because it has 100 in it

Answer 9

ohhh ok so u can find the limit

Answer 10

so it does converges

Answer 11

Sure, \(100\) is the limit of the second expression, but that doesn't mean the sequence converges to \(100\).

We still have that \(\pm\) sign to worry about. This means the sequence alternates between \(-100\) and \(100\) as \(n\) grows and grows.

The fact that \(a_n\) switches between two values forever like this means the sequence cannot converge.

Answer 12

well how do we get ride of that stupid sign?

Answer 13

i think its a postive / negative sign right or infinity

Answer 14

We don't! It tells us exactly what we want to know about this sequence: It does not converge.

Answer 15

oh oko wel thcxs for expaning that for me

Answer 16

I'm gooing with A then

Answer 17

yw

Answer 18

ready for next question?