CALC HELP PLEASE - Series, Sequences, Interest Problems?

Question

Can anyone help me with these last few problems on a review?Thanks!

1.) find a formula for the general term, an for 1/2, 1/4, 1/8, 1/16, ...

2.) Write down the first five terms of the following recursively defined sequence.
a1 = 2; an+1 = - 2an - 3 (the "n" are subscripsts)
(i got 2, -7, -16, -25, -34 which is wrong)

3.) Scott and Amanda want to purchase a house. If they invest 400 dollars per month into a mutual fund how much will they have for a downpayment after 8 years if the per annum rate of return of the mutual fund is assumed to be 9.5% compounded monthly?

4.) Evaluate
Summation from 1 to infinity of 2/(n(n+2))

5.) If the following series converges, compute its sum. Enter INF if it diverges to infinity, MINF if it diverges to minus infinity, and DIV otherwise.
Summation from 1 to infinity of (e^(-1n)-e^(-1(n+1)))

6.) Evaluate
Summation from 1 to inifinity of (-4^(n-1))/(8^n)
(i got -1/4 which is wrong)

7.) Evaluate
Summation from 1 to inifinity of (4^(n)+6^(n))/(10^n)

Answer 1

I won't be has "hard" as Cattbarf on you.
1)This you should recognize as a geometric sequence with an obvious ratio.
3)Let A be the amount you invest each month. First month you have A in the account, 2nd month you have A + interest (which is r{amount in the account the previous month}) which is A+Ar, here r is monthly interest rate. Do this for the first 5 months...you should see a series which is familiar. . solve the problem
4) Consider a partial fraction decomposition. Write off the first few terms after you do the partial fraction and you should see the answer.
5)Same as last sentence in 4.
6)& 7) First clean up the arbitrary term. Problem should be trivial then.

Answer 2

If you want homework done, go to the homework sub-section under Education.

Check your recursion formula in #2. I think they are looking for 2, -7, +11, -25.....