1. ## Sequences

1) Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity, state your answer as "INF" (without the quotation marks). If it diverges to negative infinity, state your answer as "MINF". If it diverges without being infinity or negative infinity, state your answer as "DIV".

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2. Originally Posted by nhatie
1) Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity, state your answer as "INF" (without the quotation marks). If it diverges to negative infinity, state your answer as "MINF". If it diverges without being infinity or negative infinity, state your answer as "DIV".
As the first part obviously goes to zero convergence is determined by the second part: $4 \arctan(n^2)$

What happens to $\arctan(x)$ as $x \to \infty$ ?

CB

3. will it be pi/2?

4. Originally Posted by nhatie

2) Daniel and Alice want to purchase a house. Suppose they invest dollars per month into a mutual fund. How much will they have for a downpayment after years if the per annum rate of return of the mutual fund is assumed to be percent compounded monthly?

The monthly rate of interest is $9.5/12 \%$ so now just write out the series representing the amount after 60 months.

Hint:
the first months payments will after 60 months be worth: $600(1+9.5/1200)^{60}$ dollars,
and the second months payment will be worth: $600(1+9.5/1200)^{59}$ dollars

etc.

This will give you a geometric series which you will need to sum.

CB

5. Originally Posted by nhatie
will it be pi/2?
Yes

CB

6. Originally Posted by CaptainBlack
Yes

CB
so is it a final answer? Because they said it was wrong!

7. Originally Posted by CaptainBlack
The monthly rate of interest is $9.5/12 \%$ so now just write out the series representing the amount after 60 months.

Hint:
the first months payments will after 60 months be worth: $600(1+9.5/1200)^{60}$ dollars,
and the second months payment will be worth: $600(1+9.5/1200)^{59}$ dollars

etc.

This will give you a geometric series which you will need to sum.

CB
thank you for helping. So i have to sum up to 60months? any faster way? Thank you!

8. Originally Posted by nhatie
thank you for helping. So i have to sum up to 60months? any faster way? Thank you!
Sorry, the limit of $\arctan(n^2)$ is $\pi/2$, you are effectivly asked for the limit of $4\arctan(n^2)$ which is $2\pi$.

CB

9. Originally Posted by nhatie
thank you for helping. So i have to sum up to 60months? any faster way? Thank you!
i got 46216.29: is it rite??

10. Originally Posted by nhatie
i got 46216.29: is it rite??
Yes (I have 46816.35)

CB

11. Originally Posted by nhatie
thank you for helping. So i have to sum up to 60months? any faster way? Thank you!
As I said its a finite geometric series, you can use the formula for the sum of such a series.

CB